DISEASE CHARACTERISTICS: Histologically proven hematologic malignancy with relapse after allogeneic bone marrow transplantation (BMT) or autologous BMT if no HLA matched sibling donor is available OR Histologically proven acute myeloid leukemia (AML) without an available HLA matched sibling donor and with one of the following: Failure of induction, defined as inability to obtain remission with 2 courses of induction or failure during treatment Second or greater remission OR Histologically proven acute lymphocytic leukemia (ALL) in an adult over age 15 without an available HLA matched sibling donor and with one of the following: Philadelphia chromosome positivity by cytogenetics or PCR Relapse or second or greater remission Two or more prognostic features (over age 30, WBC on presentation over 35,000/mm3, time to complete response over 4 weeks, t(4:11), or B-cell ALL) OR Histologically proven chronic myelogenous leukemia In chronic phase without an A, B, and DR unrelated matched donor OR In accelerated phase, defined as new cytogenetic abnormalities or difficulty maintaining a normal WBC due to dose limiting cytopenias (thrombocytopenias or anemia) from hydroxyurea or interferon OR In blast transformation OR Histologically proven aplastic anemia without an available HLA matched sibling donor and failure of an immunosuppressive therapy regimen using either cyclosporine, antithymocyte globulin, or both OR Histologically proven lymphoma without an available HLA matched donor and failure of at least 2 different chemotherapy regimens OR Histologically proven cutaneous T-cell lymphoma without an available HLA matched donor and failure of interferon and PUVA (psoralen and ultraviolet A radiation) OR Histologically proven myelodysplastic syndrome without an available HLA matched sibling donor and with one of the following: 5% or greater blasts in marrow Multiple cytogenetic abnormalities History of infections from neutropenia 1, 2, or 3 antigen mismatched related donor available