Pentostatin and Lymphocyte Infusion in Preventing Graft Rejection in Patients Who Have Undergone Donor Stem Cell Transplant

Inclusion Criteria: * Patients having received a preceding allogeneic transplantation from either a human leukocyte antigen (HLA)-matched related or unrelated donor are eligible for this protocol * Related donor: HLA genotypically identical at least at one haplotype and may be phenotypically or genotypically identical at the allele level at HLA A, B, C, DRB1, and DQB1 * Unrelated donor who are prospectively: * Matched for HLA-A, B, C, DRB1 and DQB1 by high resolution typing; OR * Only a single allele disparity will be allowed for HLA-A, B, or C as defined by high resolution typing * Patients with less than 50% donor CD3 peripheral blood chimerism on two separate, consecutive evaluations; the two evaluations must be at least 14 days apart OR patients with absolute decreases of donor CD3 peripheral blood chimerism of \>= 20% if the second test shows \< 50% donor CD3 cells; the two evaluations must be at least 14 days apart * Patients with evidence of disease are only eligible if the disease is stable (or persistent) in comparison to the status prior to transplantation * Patients must be tapered off systemic steroids to a dosage of less than or equal to 0.25 mg/kg/day * Patients must have persistent donor CD3 cells (\>= 5% donor CD3 cells by a deoxyribonucleic acid \[DNA\]-based assay that compares the profile of amplified fragment length polymorphisms \[ampFLP\] \[or fluorescent in situ hybridization (FISH) studies or variable number of tandem repeats (VNTR)\]) * DONOR: Alternatively to a fresh unmodified leukapheresis product, previously collected cryopreserved peripheral blood stem cells (PBSC) after mobilization with G-CSF or cryopreserved unmodified leukapheresis product from the original donor can be used; if cryopreserved product is not available, the following criteria apply for the DLI product: * DONOR: Original donor of hematopoietic cell transplantation * DONOR: Donor must give consent to leukapheresis * DONOR: Donor must have adequate veins for leukapheresis or agree to placement of central venous catheter (femoral or subclavian) * DONOR: Donor must be medically fit to undergo the apheresis procedure (institutional guidelines for apheresis) Exclusion Criteria: * Current grade II to IV acute GVHD or extensive chronic GVHD * Karnofsky score \< 50% * Pediatric criteria * Lansky play-performance score \< 40 * Evidence of relapse or progression of disease after transplantation * Prior recipient of cord blood * DONOR: Donors who are not suitable for medical reasons to donate peripheral blood mononuclear cells (PBMC) by continuous centrifugation according to the criteria of the American Association of Blood Banks (AABB) * DONOR: Pregnancy * DONOR: Human immunodeficiency virus (HIV) or human T-lymphotrophic virus (HTLV) infection * DONOR: Recent immunization may require a delay