No intent to use myeloablative conditioning regimens.
Patient deemed to be suitable candidate for myeloablative or reduced intensity conditioning allogeneic HSCT using PBSC or marrow as stem cell source
Participants must be recipients of an allogeneic bone marrow or stem cell transplantation with myeloablative or reduced intensity conditioning regimens
Have undergone allogeneic stem cell transplantation (alloSCT) from any donor source (matched unrelated donor, sibling, haplo-identical) using bone marrow, peripheral blood stem cells, or cord blood. Recipients of non-myeloablative, myeloablative, and reduced intensity conditioning are eligible
Participant is considered a suitable candidate for HCT and has an acceptable source of allogeneic donor stem cells, as defined per institutional practice (allogeneic HCT for any donor source [matched sibling, unrelated donor (URD), mismatched URD, related haploidentical, or umbilical cord blood] and any graft source [umbilical cord, BM, peripheral blood (PB)], and any conditioning [myeloablative conditioning (MAC), reduced intensity conditioning (RIC), or non-myeloablative conditioning (NMA)] will be permitted).
Participants may receive either a myeloablative or a non-myeloablative (reduced-intensity) conditioning regimen
Recipient of a myeloablative or non-myeloablative allogeneic hematopoietic stem cell transplant (HSCT):\r\n* Conditioning regimen to be prescribed at investigators discretion, but will be prospectively defined as myeloablative or non-myeloablative
Patients that have undergone immunotherapy in combination with non-myeloablative chemotherapy
Prior myeloablative transplant containing full dose TBI (greater than  Gray [Gy])
Any prior myeloablative transplant within the last  months
Patients who have received Y- ibritumomab (Zevalin) or I- tositumomab (Bexxar), as part of their salvage therapy are not eligible for myeloablative umbilical cord blood transplant
Will undergo first allogeneic hematopoietic stem cell transplantation (HSCT) for their malignancy. Conditioning may have been either conventional myeloablative (MAC) or reduced intensity conditioning (RIC)
Patients >=  years and <  years are also included if they are not candidates for myeloablative conditioning regimens due to comorbidities
Any conditioning regimen (non-myeloablative, myeloablative, or reduced intensity) is acceptable.
Diagnosis: Patients with disorders affecting the hematopoietic system that are inherited, acquired, or result from myeloablative treatment.
Use of myeloablative conditioning regimen
Recipients of allogeneic stem cell transplantation with myeloablative or non-myeloablative conditioning regimens; alternative donor transplants (umbilical cord blood and haploidentical) are allowed
Have undergone Allogeneic Stem Cell Transplanttaion (alloSCT) from any donor source (matched unrelated donor, sibling, haplo-identical) using bone marrow, peripheral blood stem cells, or cord blood. Recipients of non- myeloablative, myeloablative, and reduced intensity conditioning are eligible
Deemed to be not otherwise eligible for a myeloablative hematopoietic cell transplant; high risk characteristics for a myeloablative transplant include age >  years and a HCT comorbidity index > 
Less than  months since prior myeloablative transplant
Patients with HM who have undergone myeloablative systemic therapy are ineligible to participate in this study.
Must be >=  months after prior myeloablative transplant, if applicable
Patients with or without previous myeloablative autologous transplant
Any donor type (e.g., related, unrelated) or stem cell source (bone marrow, peripheral blood, cord blood); recipients of non-myeloablative and myeloablative transplants are eligible
First allogeneic hematopoietic stem cell transplantation (HSCT) using myeloablative conditioning (MAC), non-myeloablative (NMA), or reduced-intensity conditioning (RIC) preparative regimens.
Prior myeloablative or non-myeloablative allogeneic hematopoietic stem cell transplant using either bone marrow or peripheral blood stem cells or single or double cord blood within  months.
Prior myeloablative or non-myeloablative autologous or allogeneic hematopoietic stem cell transplant using the marrow, peripheral blood stem cells or single or double umbilical cord blood
STEP : Within  days of study entry: Patients with a history of bone marrow disorders including hematological malignancies and aplastic anemia, myelodysplastic Syndrome (MDS) and myeloproliferative disorder (MPD) planning to undergo allogeneic HSCT with reduced intensity or myeloablative conditioning regimens
Patients ineligible to receive full myeloablative conditioning regimen for allogeneic hematopoietic progenitor cell transplant due to age or comorbidities
Prior myeloablative or non-myeloablative allogeneic hematopoietic stem cell transplant using either bone marrow or peripheral blood stem cells or single or double cord blood within  months
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
Patients developing aGvHD after ablative or non-myeloablative or reduced intensity conditioning will be eligible
Myeloablative transplant within the last  months
If >  years old, prior myeloablative transplant within the last  months
If =<  years old, prior myeloablative transplant within the last  months; if >  years old prior myeloablative allotransplant or autologous transplant
Patients who have received Y- ibritumomab (zevalin) or I- tostumomab (bexxar), as part of their salvage therapy are not eligible for myeloablative umbilical cord blood transplant
Second BMT: must be >=  months after prior myeloablative transplant
If =<  years old, prior myeloablative transplant within the last  months; if > years old prior myeloablative allotransplant or autologous transplant
Patients are eligible  weeks after myeloablative therapy with autologous stem cell transplant (timed from start of vorinostat); patients must meet adequate bone marrow function definition post-myeloablative therapy; patients who received stem cell reinfusion following non-myeloablative therapy are eligible once they meet peripheral blood count criteria
Prior myeloablative allotransplant
Patients who have received yttrium (Y)- ibritumomab (Zevalin) or iodine (I)- tositumomab (Bexxar), as part of their salvage therapy are not eligible for myeloablative UCB transplant
Myeloablative or non-myeloablative allogeneic hematopoietic cell transplantation
No prior myeloablative therapy or hematopoietic cell transplantation
Must be >=  months after prior myeloablative transplant, if applicable
Has received prior allogeneic transplants or who are planned to undergo umbilical cord blood transplant, receive ex vivo T-cell-depleted hematopoietic stem cells (HSCs), received any in vivo T-cell depleting antibodies, or non-myeloablative conditioning.
Applicable disease and eligible for myeloablative SCT
Recipients of -/ human leukocyte antigen (HLA) matched adult donor allogeneic stem cell transplantation with myeloablative or non-myeloablative conditioning regimens
Patients with uncontrolled infections for whom myeloablative hematopoietic stem cell transplant (HCT) is considered contraindicated by the consulting infectious disease physician (upper respiratory tract viral infection does not constitute an uncontrolled infection in this context)
Prior myeloablative transplant containing full dose TBI (greater than  Gy)
Myeloablative or non-myeloablative allogeneic hematopoietic cell transplant
Prior myeloablative transplant within previous  months of study enrollment
Prior allogeneic or autologous stem cell transplant using a myeloablative busulfan or total body radiation containing conditioning regimen defined as busulfan-based using a total dose of >=  mg/kg given by mouth or >=  mg/kg given IV; or a total-body irradiation (>  Gy)
Standard pediatric indications for myeloablative transplantation for patients undergoing HSCT at Childrens National Medical Center per institutional guidelines
Age greater than or equal to  year but less than or equal to  years (myeloablative regimen ); eligibility for pediatric patients will be determined in conjunction with an MD Anderson Cancer Center (MDACC) pediatrician; patients >  but <  years who have a performance status of  or  and no comorbidities may receive the myeloablative regimen  at the discretion of the investigator(s)
Prior myeloablative transplant within the last  months
Prior myeloablative or non-myeloablative allogeneic hematopoietic stem cell transplant using either bone marrow or peripheral blood stem cells or single or double cord blood within  months.
Patients are eligible  weeks after myeloablative therapy with autologous stem cell transplant (timed from start of protocol therapy); patients must meet adequate bone marrow function definition post-myeloablative therapy; patients who received stem cell reinfusion following non-myeloablative therapy are eligible once they meet peripheral blood count criteria; patients status post-allogeneic stem cell transplant are excluded unless they are >  year post transplant, have been off all immunosuppressive therapy for more than  months and do not have active graft-versus-host disease (GVHD)
Patients are eligible  weeks after date of autologous hematopoietic stem cell infusion following myeloablative therapy (timed from first day of this protocol therapy).
Patients who have received an autologous hematopoietic stem cell infusion to support non-myeloablative therapy (such as I-MIBG) are eligible at any time as long as they meet the other criteria for eligibility.
Donor cellular engraftment of at least .% from the non-myeloablative procedure and prior to the first infusion
Subjects who had histopathologically confirmed overall grade  GVHD lasting longer than  days, from the non-myeloablative therapy, are not eligible
Acute lymphoblastic leukemia (ALL) \r\n * ALL patients will be eligible if they fail to attain an initial remission, if they relapse within  year following the discontinuation of chemotherapy, or if they have other unfavorable prognostic features such that a stem cell transplant (SCT) would offer a significant survival advantage; patients must be in complete remission or have =< % blasts in bone marrow at the time of admission to the HSCT unit; patients in complete remission will preferentially receive a myeloablative transplant from a related or unrelated donor; however, patients will be eligible for this study if a suitable related or unrelated donor cannot be identified, the amount of time required to identify a suitable donor is deemed unacceptable, or the patient is not eligible for a myeloablative transplant regimen\r\n * Patients who relapse following a myeloablative transplant, but cannot receive DLI (e.g. cord blood recipients, graft loss) will also be eligible; such patients must be >=  months post initial transplant, achieve a CR or have =< % blasts in the bone marrow prior to admission to the HSCT unit
Meet standard criteria as defined by the institution for a myeloablative allogeneic stem cell transplantation, with myeloablative defined as using conditioning regimens containing:\r\n* Total-body irradiation (TBI) >=  cGy, or \r\n* Busulfan >= . mg/kg
Myeloablative preparative regimen (for SAA any conditioning therapy allowed)
Conditioning Regimen: Patients expecting to receive any type of myeloablative HSCT conditioning regimen are eligible
Patients must be receiving a fractionated total body radiation (FTBI) based- myeloablative conditioning regimen; (acceptable conditioning regimens include total body irradiation [TBI] + cyclophosphamide or TBI + etoposide)
Patients designated to undergo myeloablative or intermediate intensity allogeneic peripheral blood or bone marrow hematopoietic cell transplantation; consent will be obtained prior to admission for HSCT; patients receiving any donor source of stem cells are eligible; eligible conditioning regimens are those defined as myeloablative by the American Society of Blood and Marrow Transplantation (ASBMT) consensus criteria as well as the combination of fludarabine with melphalan (- mg/mg^)
Recipients of allogeneic hematopoietic cell transplantation (HCT) after either myeloablative or reduced intensity conditioning regimens; any donor source of stem cells is eligible
All conditioning regimens will be eligible (in case of allogeneic HCT, patient could have received myeloablative or non-myeloablative/reduced-intensity conditioning)
Recipients of allogeneic hematopoietic cell transplantation (HCT) after either myeloablative or reduced intensity conditioning regimens; any donor source of stem cells is eligible
Prior myeloablative or non-myeloablative allogeneic hematopoietic stem cell transplant using either bone marrow or peripheral blood stem cells within  months
Myeloablative preparative regimen (i.e., >= TBI . Gy, >= busulfan (BU) . mg/kg PO, >= BU . mg/kg intravenously (IV), >= treosulfan  g/m^ IV) according to investigational study or standard treatment plan; other \myeloablative\ preparative regimens are acceptable as long as they are approved by the principal investigator or designee
Less than  months from myeloablative conditioning for autologous transplantation
Planned myeloablative conditioning regimen
Patients who have undergone a non-myeloablative stem cell transplant must have > % donor hematopoiesis within  days of study enrollment; chimerism within  days of study entry must be greater than, equal to, or no more than % less than the chimerism measured at approximately day + (if performed)
Patients who have undergone a non-myeloablative stem cell transplant must have > % donor lymphoid hematopoiesis within  days of study enrollment
ELIGIBILITY FOR MYELOABLATIVE CONDITIONING
Myeloablative preparative regimen
Less than  months from myeloablative conditioning for autologous transplantation (if applicable)
Be scheduled to receive one of  myeloablative conditioning regimens (defined in population) followed by allogeneic SCT for hematological malignancy.