Donor T Cells After Donor Stem Cell Transplant in Treating Patients With Hematologic Malignancies

Inclusion Criteria: * INCLUSION CRITERIA PRIOR TO TRANSPLANT: * The clinical trial will be offered to all high risk (defined 3 below) patients with hematologic malignancies who require stem cell transplants as part of their standard of care using matched related or unrelated donors * Patients with high risk myeloid or lymphoid malignancies at stem cell transplant following American Society for Blood and Marrow Transplantation (ASBMT) criteria, including but not limited to conditions listed; these criteria apply BEFORE cyto-reductive therapy given within 28 days of planned conditioning: * Refractory acute myelogenous or lymphoid leukemia * Relapsed acute myelogenous or lymphoid leukemia * Myelodysplastic syndromes with 5% or more blasts * Chronic myelogenous leukemia in chronic phase 3 or more, blast phase presently, or second accelerated phase * Recurrent or refractory malignant lymphoma or Hodgkin's disease with less than a partial response at transplant * High risk chronic lymphocytic leukemia defined as no response or stable disease to the most recent treatment regimen * DONORS: Matched related or unrelated donor stem cell transplant (SCT) matched at human leukocyte antigen (HLA) A- B, C, and DRB1 by molecular methods; 7 of 8 matched donor acceptable for related donors * T-cell depletion with anti-thymocyte globulin (ATG) (rabbit or horse) or at least 30 mg of alemtuzumab total in the conditioning regimen * Immune suppression; planned post-transplant immune suppression should include tacrolimus or cyclosporin monotherapy (i.e., calcineurin inhibitor or CN) for alemtuzumab regimens and a second immune suppressant for ATG treated patients; other agents may be used if CN intolerance or toxicity occurs post-transplant * Zubrod performance status (PS) 0-2 or equivalent Karnofsky PS * Eligible for allogeneic transplant in the treating physicians' judgment and by institutional standards * ELIGIBILITY TO RECEIVE DLI POST-TRANSPLANT: * Donor lymphocytes available or able to be collected * No evidence of disease by standard morphology; minimal residual disease or molecular evidence of disease will not exclude * Absolute neutrophil count \>= 500/μl * Platelet count \>= 20,000/μl without transfusion for 7 days * Serum glutamic oxaloacetic transaminase (SGOT) and serum glutamate pyruvate transaminase (SGPT) =\< 5 x upper limit of normal (ULN) * Bilirubin =\< 3 x ULN * No evidence of grade II or higher acute GVHD or chronic GVHD at initiation of first DLI * No systemic corticosteroids or immunosuppressive drugs (topical acceptable); replacement steroids for adrenal insufficiency are not excluded Exclusion Criteria: * EXCLUSION CRITERIA PRIOR TO TRANSPLANT: * Pregnant or lactating females * Hepatitis B with positive viral load prior to transplant conditioning or hepatitis C virus * Human immune deficiency virus * Psychiatric illness that may make compliance to the clinical protocol unmanageable or may compromise the ability of the patient to give informed consent * Creatinine \>= 2.0 mg/dL * SGOT and SGPT \>= 5 x ULN; liver biopsy preferred for such patients * Bilirubin \>= 3 x ULN (unless Gilbert's syndrome) * Diffusing capacity of the lung for carbon monoxide (DLCO) \< 50% corrected for hemoglobin * Left ventricular ejection fraction or shortening fraction \< 40% * Unlikely to be able to procure additional donor lymphocytes