Patients with an immunodeficiency that existed prior to diagnosis, such as primary immunodeficiency syndromes, organ transplant recipients and children on current systemic immunosuppressive agents are not eligible Patients with an immunodeficiency that existed prior to diagnosis such as primary immunodeficiency syndromes or organ transplant recipients are not eligible Organ transplant recipients other than bone marrow transplant De novo recipients of a primary orthotopic liver transplant from a deceased or living donor Recipients of donor/recipient ABO incompatible grafts. Organ transplant recipients Hypersensitivity to pembrolizumab or any of its recipients Hypersensitivity to pembrolizumab or any of its recipients Use of two forms of contraception with less than a % failure rate or abstinence by all transplanted patients for a minimum of month after the last dose of Idelalisib; for the first days post?transplant, transplant recipients should be encouraged to use non?hormonal contraceptives due to the potential adverse effect of hormones on bone marrow engraftment RECIPIENTS RECIPIENTS: Recipients of prior autologous or allogeneic transplant are eligible, as long as at least months have passed since the transplant, and the patient fulfills other eligibility criteria Recipients will have satisfactory organ function (excluding bone marrow) and will have a Karnofsky activity assessment > % and will have: Recipients will fall under one of the following disease categories: Recipients will sign informed consent approved by the Committee on the Use of Human Subjects at the University of Minnesota Subjects who have a known immunocompromised condition (HIV+, use of immunosuppressive medications or systemic steroids, organ transplant recipients) Organ transplant recipients other than bone marrow transplant; Patients with an immunodeficiency that existed prior to diagnosis, such as primary immunodeficiency syndromes, organ transplant recipients and children on current systemic immunosuppressive agents are not eligible F FLT CANDIDATE TRANSPLANT RECIPIENT: Meets criteria for transplant recipients For recipients with CLL or PLL, treatment failure for a specified therapy is defined as relapse within months or failure to achieve remission \r\n* Recipients who are ineligible for a specified therapy (e.g., due to refractory cytopenias) may be considered for enrollment in this protocol\r\n* Recipients who have a p/p deletion who have never received fludarabine will be eligible\r\n* Recipients who have had Richters transformation who have not received prior chemotherapy for their CLL will be eligible Use of two forms of contraception with less than a % failure rate or abstinence by all transplanted participants for months after the first dose of study therapy; for the first days post-transplant, recipients should be encouraged to use nonhormonal contraceptives due to the potential adverse effect of hormones on bone\r\nmarrow engraftment Single solid organ recipients (kidney only) Autologous transplant recipients with multiple myeloma or lymphoma (both Hodgkins and non-Hodgkins types) will be eligible to participate in the study; those with other disease types will be excluded Allogeneic transplant recipients undergoing ablative transplants will also be eligible to participate; those receiving nonablative regimens (a small proportion of allogeneic transplant recipients at UWCCC) will be excluded CARE-RECIPIENTS CARE-RECIPIENTS: Has an additional cancer diagnosis Allogeneic transplant recipients undergoing fully ablative transplants Those receiving reduced intensity regimens (a small proportion of allogeneic transplant recipients at UWCCC) Bone marrow transplant recipients. Allogeneic HSCT recipients who are - months post-transplant Allogeneic HSCT recipients who are - months post-transplant Patients with clinically significant and unstable renal and/or liver disease (eg, transplant recipients in rejection) Recipients with AML will be recruited by personnel at the transplant centers (TC) who are candidates for URD HCT