Known history of allergy to Captisol (a cyclodextrin derivative used to solubilize carfilzomib) Known history of allergy to Captisol (a cyclodextrin derivative used to solubilize carfilzomib) Known allergy to Captisol® (a cyclodextrin derivative used to solubilize carfilzomib). Known history of allergy to Captisol (a cyclodextrin derivative used to solubilize CFZ), or similar chemical or biologic composition to bendamustine or other agents used in the study Known history of allergy to Captisol (a cyclodextrin derivative used to solubilize carfilzomib) Must not have any known history of allergy to Captisol® (a cyclodextrin derivative used to solubilize carfilzomib). Known history of allergy to Captisol (a cyclodextrin derivative used to solubilize carfilzomib) Patients who have a known history of allergy to Captisol (a cyclodextrin derivative used to stabilize carfilzomib) are NOT eligible for participation Known history of allergy to Captisol (a cyclodextrin derivative used to solubilize carfilzomib) History of allergy to Captisol (a cyclodextrin derivative used to solubilize carfilzomib) Known history of allergy to Captisol (a cyclodextrin derivative used to solubilize carfilzomib) Known history of allergy to Captisol (a cyclodextrin derivative used to solubilize carfilzomib) Known history of allergy to Captisol (a cyclodextrin derivative used to solubilize carfilzomib) No known history of allergy to Captisol (a cyclodextrin derivative used to solubilize carfilzomib) Known allergy to Captisol (a cyclodextrin derivative used to solubilize carfilzomib) Known history of allergy to Captisol® (a cyclodextrin derivative used to solubilize carfilzomib) Known history of allergy to Captisol (a cyclodextrin derivative used to solubilize carfilzomib) Known history of allergy to Captisol® (a cyclodextrin derivative used to solubilize carfilzomib). Known history of allergy to Captisol (a cyclodextrin derivative used to solubilize carfilzomib) Known history of allergy to Captisol® (a cyclodextrin derivative used to solubilize carfilzomib) Known allergies to carfilzomib or Captisol® (a cyclodextrin derivative used to solubilize carfilzomib) Known history of allergy to Captisol (a cyclodextrin derivative used to solubilize carfilzomib) Known history of allergy to Captisol(a cyclodextrin derivative used to solubilize carfilzomib). Known history of allergy to Captisol® (a cyclodextrin derivative used to solubilize carfilzomib) fludarabine, cladribine, or clofarabine within 3 months of enrollment Patients with a known hypersensitivity to treosulfan and/or fludarabine History of severe immediate hypersensitivity reaction to cyclophosphamide, fludarabine, or aldesleukin. Contraindication to cyclophosphamide or fludarabine chemotherapy History of hypersensitivity to cyclophosphamide, fludarabine, dimethyl sulfoxide (DMSO) or IL-2 History of severe immediate hypersensitivity reaction to cyclophosphamide, fludarabine, or aldesleukin Subject has known sensitivity and immediate hypersensitivity to any components of AMG 119 or conditioning regimen (cyclophosphamide and fludarabine). Contraindication to cyclophosphamide or fludarabine chemotherapy Prior use of clofarabine or fludarabine History of severe immediate hypersensitivity reaction to cyclophosphamide or fludarabine Previously known hypersensitivity to any of the agents used in this study; known sensitivity to busulfan or fludarabine History of severe hypersensitivity to nivolumab, cyclophosphamide, fludarabine, interleukin-2, or any excipient Washout period of at least 14 days after any approved or experimental tumor directed therapy prior to start of cyclophosphamide and fludarabine History of severe immediate hypersensitivity reaction to cyclophosphamide, aldesleukin, or fludarabine fludarabine, cladribine, or clofarabine within 3 months of enrollment Received any investigational agent within the 14 days before the start of study treatment (1st dose of fludarabine phosphate [fludarabine]) History of hypersensitivity to cyclophosphamide, fludarabine or IL-2. History of severe immediate hypersensitivity reaction to cyclophosphamide, fludarabine or aldesleukin History of severe immediate hypersensitivity reaction to cyclophosphamide or fludarabine B-cell (B)-chronic lymphocytic Leukemia (CLL)\r\n* Relapse/progression after two previous regimens\r\n* No response or progression =< 6 months after fludarabine (fludarabine phosphate) or bendamustine based regimen\r\n* Progression within 24 months of a fludarabine and alkylator combination regimen\r\n* Progression after any regimen in the presence of deletion (del)17p or mutated tumor protein p53 (TP53)\r\n* Persons with high grade lymphoma transformation Any known contraindications to cyclophosphamide, fludarabine, etoposide, bendamustine, cetuximab or tocilizumab Any known contraindications to cyclophosphamide, fludarabine, etoposide, cetuximab or tocilizumab Patients who relapse after receiving a one or more courses of fludarabine, bendamustine, cytoxan, rituxan, chlorambucil, or campath based therapy Must receive a myeloablative or reduced intensity conditioning regimen for stem cell transplant (SCT) as defined by the Center for International Blood and Bone Marrow Transplant Research (CIBMTR)\r\n* Cyclophosphamide (Cy) and single dose total body irradiation\r\n* Fludarabine (Flu) and busulfan\r\n* Fractionated total body irradiation (TBI) and cyclophosphamide\r\n* Busulfan and cyclophosphamide History of severe immediate hypersensitivity reaction to cyclophosphamide, fludarabine, or aldesleukin Chronic lymphocytic leukemia/small lymphocytic lymphoma (CLL/SLL): Must be refractory to fludarabine (fludarabine phosphate) or fail to have a complete or partial response after therapy with a regimen containing fludarabine (or another nucleoside analog, e.g. cladribine [2-CDA], pentostatin) or experience disease relapse within 12 months after completing therapy with a regimen containing fludarabine (or another nucleoside analog) History of hypersensitivity to cyclophosphamide, fludarabine or IL-2 Fludarabine based therapy within 6 months of enrollment History of allergic reactions to chemotherapy agents used in this protocol as part of lymphodepletion regimen (fludarabine and cyclophosphamide) A treatment regimen containing cytotoxic agents (eg, fludarabine, pentostatin, cladribine, cyclophosphamide, chlorambucil, bendamustine) AND Pregnant women are excluded from this study; females of child bearing potential must have a negative pregnancy test within 14 days of study treatment; breastfeeding must be discontinued before beginning fludarabine (fludarabine phosphate) At least 14 days must have elapsed since any prior systemic therapy at the time the patient starts the cyclophosphamide and fludarabine (fludarabine phosphate) conditioning regimen, and patients’ toxicities must have recovered to a grade 1 or less (except for toxicities such as alopecia or vitiligo) With known hypersensitivity to treosulfan or fludarabine (fludarabine phosphate) Fludarabine or Campath within 12 months prior to study entry Able to tolerate high-dose cyclophosphamide, fludarabine and high-dose IL-2 Able to tolerate high-dose cyclophosphamide, fludarabine, and high-dose IL-2 T-cell depletion with anti-thymocyte globulin (ATG) (rabbit or horse) or at least 30 mg of alemtuzumab total in the conditioning regimen; acceptable conditioning regimens include but are not limited to fludarabine/melphalan/alemtuzumab; fludarabine/busulfan/alemtuzumab; fludarabine/melphalan/ATG; fludarabine/busulfan/ATG Fludarabine-based chemotherapy within 6 months Prior treatment with fludarabine or alemtuzumab based regimens. considered inappropriate for fludarabine-based therapy B-chronic lymphocytic leukemia (CLL), small lympho(plasma)cytic lymphoma (B-SLL, B-LPL)\r\n* Relapse/progression after fludarabine (fludarabine phosphate) and at least one other salvage regimen or 2 standard regimens\r\n* If 17p deletion present, one standard regimen is sufficient Patients with B-Cell CLL or PLL who:\r\n* Failed to meet National Cancer Institute (NCI) Working Group criteria 2 for complete or partial response after 2 cycles of therapy with regimen containing fludarabine (or another nucleoside analog, e.g. cladribine [2-CDA], pentostatin) or with disease relapse within 12 months after completing therapy with a fludarabine (or another nucleoside analog) containing regimen\r\n* Failed FCR or pentostatin/cyclophosphamide/rituximab (PCR) combination chemotherapy at any time point\r\n* Patients with novo or acquired “17p deletion” cytogenetic abnormality; patients should have received induction treatment but could be transplanted in 1st CR Not a candidate for fludarabine therapy based on either: Patient must have documented CR or CRp after 1 or 2 cycles of fludarabine + cytarabine Previously untreated patients who have been counseled on approved alternative therapeutic options. Not a candidate for fludarabine/cyclophosphamide/rituximab (FCR) or has preference to not receive chemotherapy. History of severe immediate hypersensitivity reaction to cyclophosphamide or fludarabine phosphate (fludarabine) The patient has received Fludarabine, Clofarabine or Cloretazine within 12 months preceding the ASCI treat-ment. Fludarabine or Campath within 12 months prior to study entry History of severe immediate hypersensitivity reaction to cyclophosphamide or fludarabine (fludarabine phosphate) History of severe immediate hypersensitivity reaction to cyclophosphamide or fludarabine Patient must receive any one of the following conditioning regimens: total body radiation (single or fractionated dose)/cyclophosphamide, busulfan/cyclophosphamide, or fludarabine/busulfan/lymphocyte immune globulin (ATGAM/thymoglobulin [thymo]) Subjects will be eligible if their planned conditioning regimen for allogeneic HCT consists of one of the two following standard reduced intensity conditioning regimens:\r\n* FLU/MEL: fludarabine phosphate (fludarabine) 120 to 180 mg/m^2; melphalan hydrochloride (melphalan) =< 150 mg/m^2\r\n* FLU/BU: fludarabine 120 to 180 mg/m^2; busulfan =< 8 mg/kg orally or =< 6.4 mg/kg intravenously Participants must be designated to undergo reduced intensity allogeneic peripheral blood hematopoietic stem cell transplantation (HSCT); consent will be obtained prior to admission for HSCT; the following HSCT conditions must be planned:\r\n* Donors must be 8/8 HLA-matched (at the allele level) as defined by matching at HLA-A, -B, -DR and –C who pass institutional standard to serve as a peripheral blood stem cell donor\r\n* Donor grafts must be granulocyte colony-stimulating factor (G-CSF) mobilized peripheral blood stem cells with dose and apheresis logistics at the discretion of institutional standard\r\n* Conditioning therapy will be one of the following 3 options:\r\n** Fludarabine/melphalan where fludarabine is >= 90 mg/m^2 intravenously (IV) total dose and melphalan is 100-140 mg/m^2 IV total dose; exact logistics of administration are at the discretion of institutional standard\r\n** Fludarabine/busulfan where fludarabine is >= 90 mg/m^2 IV total dose and busulfan = 6.4 mg/kg IV total dose; exact logistics of administration are at the discretion of institutional standard\r\n** Fludarabine/busulfan where fludarabine is >= 90 mg/m^2 IV total dose and busulfan is dosed to achieve area under the curve (AUC) of 4000 umol/min based on a pharmacokinetics determined from a test dose; exact logistics are at the discretion of institutional standard\r\n* GVHD prophylaxis is comprised of tacrolimus/short course methotrexate as defined by tacrolimus started prior to day 0 of HSCT and methotrexate given after HSCT on days +1, +3 and +6 +/- +11 at a dose of 5-10 mg/m^2 IV; exact logistics are at the discretion of the treating institution History of severe immediate hypersensitivity reaction to any of the agents used in this study Known hypersensitivity to one or more of the study agents used Is unable to receive any of the agents used in this study due a history of severe immediate hypersensitivity reaction (e.g. hypersensitivity to dimethyl sulfoxide (DMSO)) History of severe immediate hypersensitivity reaction to any of the agents used in this study History of severe immediate hypersensitivity reaction to any of the agents used in this study History of severe immediate hypersensitivity reaction to any of the agents used in this study History of severe immediate hypersensitivity reaction to any of the agents used in this study History of severe immediate hypersensitivity reaction to any of the agents used in this study History of severe immediate hypersensitivity reaction to any of the agents used in this study Known hypersensitivity to any of the study agents used Previously known hypersensitivity to any of the agents used in this study History of severe immediate hypersensitivity reaction to any of the agents used in this study History of severe immediate hypersensitivity reaction to any of the agents used in this study Previously known hypersensitivity to any of the agents used in this study History of severe immediate hypersensitivity reaction to any of the agents used in this study History of severe immediate hypersensitivity reaction to any of the agents used in this study History of severe immediate hypersensitivity reaction to any of the agents used in this study History of severe immediate hypersensitivity reaction to any of the agents used in this study Previously known hypersensitivity to any of the agents used in this study History of severe immediate hypersensitivity reaction to any of the agents used in this study Known hypersensitivity to any of the study agents used History of severe immediate hypersensitivity reaction to any of the agents used in this study History of severe immediate hypersensitivity reaction to any of the agents used in this study Previously known hypersensitivity to any of the agents used in this study Previously known hypersensitivity to any of the agents used in this study History of severe immediate hypersensitivity reaction to any of the agents used in this study Known hypersensitivity to any of the study agents used History of severe immediate hypersensitivity reaction to any of the agents used in this study History of severe immediate hypersensitivity reaction to any of the agents used in this study History of severe immediate hypersensitivity reaction to any of the agents used in this study History of severe immediate hypersensitivity reaction to any of the agents used in this study History of severe immediate hypersensitivity reaction to any of the agents used in this study History of severe immediate hypersensitivity reaction to any of the agents used in this study History of severe, immediate hypersensitivity reaction attributed to aminoglycosides