Prior liver transplant TRANSPLANT PATIENTS: all patients undergoing planned allogeneic transplant (both malignant and non-malignant diagnoses) Patients with prior history of or active severe (grade 3 or 4) acute graft-versus-host disease (GVHD) Patients may have received prior allogeneic transplant or autologous transplant; however, patients with prior allogeneic bone marrow transplant will be eligible only if both of the following conditions are met:* The transplant must have been performed >= 90 days prior to registration* The patient must not have >= grade 2 acute graft versus host disease (GvHD) or either moderate or severe limited chronic GvHD within 14 days prior to registration Allogeneic stem cell transplantation is allowed provided the patient is >= 1 year from transplant at time of registration, is not on immunosuppressive therapy to treat/prevent graft-versus-host disease, has no evidence of active graft versus host disease, and no evidence of active infection Active graft-versus-host disease (GVHD) following allogeneic stem cell transplant for non-AML condition (ex. MDS, MPN, lymphoid malignancy, aplastic anemia) requiring ongoing use of immunosuppressants Patients who are receiving cyclosporine, tacrolimus or other agents to prevent graft-versus-host disease post bone marrow transplant are not eligible for this trial Prior autologous and/or allogeneic transplant is permitted although transplant must have occurred greater than 90 days prior to registration Previous allogeneic bone marrow transplant Patients who are receiving cyclosporine, tacrolimus or other agents to prevent graft-versus-host disease post bone marrow transplant are not eligible for this trial Patients with history of organ transplant INCLUSION CRITERIA FOR STRATUM C: Patient must be:* >= 12 weeks since autologous bone marrow/stem cell transplant prior to enrollment* >= 5 years since allogeneic bone marrow transplant prior to enrollment with no evidence of active graft versus (vs.) host disease cHL COHORT ONLY: history of allogeneic transplant Prior allogeneic bone marrow transplant Patients who are receiving cyclosporine, tacrolimus or other agents to prevent graft-versus-host disease post bone marrow transplant are not eligible for this trial Anti-GVHD agents post-transplant: Patients who are receiving cyclosporine, tacrolimus or other agents to prevent graft-versus-host disease post bone marrow transplant are not eligible for this trial Patients who are receiving cyclosporine, tacrolimus or other agents to prevent graft-versus-host disease post bone marrow transplant are not eligible for this trial Patients are not eligible if they have had or are planned for solid organ transplant; patients who have received allogeneic hematopoietic stem cell transplant are eligible if:* The transplant occurred at least 90 days prior to registration, * Patient has no prior acute graft versus host disease (GVHD), and * Within 48 hours of registration, patient demonstrates at least 90% engraftment, defined as: absolute neutrophil count (ANC) >= 500 mcl, measured over 3 consecutive days or 1 day with an ANC >= 1,000 mcl, or platelets >= 50,000 mcl measured, wherein the patient did not receive any platelet transfusions within 7 days prior to laboratory assessment No evidence of active graft versus (vs.) host disease and >= 2 months must have elapsed since transplant Patients who are receiving cyclosporine, tacrolimus or other agents to prevent either graft-versus-host disease post bone marrow transplant or organ rejection post-transplant are not eligible for this trial Patients with prior history of severe (grade III or IV) acute GVHD even if resolved if post-transplant Patients who are receiving cyclosporine, tacrolimus or other agents to prevent graft-versus-host disease post bone marrow transplant are not eligible for this trial Anti-GVHD or agents to prevent organ rejection post-transplant; patients who are receiving cyclosporine, tacrolimus, or other agents to prevent either graft-versus-host disease post bone marrow transplant or organ rejection post-transplant are not eligible for this trial; at least 3 half-lives must have elapsed after the last dose of GVHD medications (meds) Patients, who relapsed 6 months after bone marrow transplant and have no evidence of active graft versus host disease and are off systemic immunosuppressant medications for at least 2 months and have received hypomethylating agents (HMA) therapy before or after transplant and meet other eligibility criteria of progression after at least 4 months of DNMTi therapy, are eligible to be enrolled in this clinical trial Patients must not have any history of organ transplant that requires use of immunosuppressives Prior liver transplant Patients who are receiving cyclosporine, tacrolimus or other agents to prevent graft-versus-host disease post bone marrow transplant are not eligible for this trial Patients who are receiving cyclosporine, tacrolimus or other agents to prevent graft-versus-host disease post bone marrow transplant are not eligible for this trial