Fludarabine, Cyclophosphamide, and Total-Body Irradiation Followed by Cyclosporine and Mycophenolate Mofetil in Treating Patients Who Are Undergoing a Donor Umbilical Cord Blood Transplant for Hematologic Cancer

DISEASE CHARACTERISTICS: * Diagnosis of 1 of the following hematologic malignancies: * Acute myeloid leukemia (AML) with or without history of myelodysplastic syndromes, meeting 1 of the following criteria: * In first complete remission (CR-1) with unfavorable cytogenetics and/or achieved CR-1 after ≥ 1 course of induction therapy * Secondary or treatment-related AML * In second or further complete remission * Relapsed with ≤ 20% blasts in the bone marrow AND no circulating blasts * Acute lymphoblastic leukemia (ALL), meeting 1 of the following criteria: * In CR-1 with unfavorable cytogenetics or elevated WBC at presentation OR failed to achieve CR-1 after ≥ 4 weeks of induction therapy * In second or further complete remission * Relapsed with ≤ 20% blasts in the bone marrow AND no circulating blasts * Other acute leukemic variants allowed at the discretion of the principal investigator * Chronic myelogenous leukemia (CML), meeting 1 of the following criteria: * In first chronic phase AND refractory to or unable to tolerate imatinib mesylate * In second or further chronic phase * In first or second accelerated phase * Myelodysplastic syndromes with intermediate 2- or high-risk International Prognosis Scoring System (IPSS) score, including any of the following: * Refractory anemia * Refractory anemia with excess blasts * Chronic myelomonocytic leukemia * Myeloproliferative disorders with poor prognosis, including any of the following: * Myelofibrosis with myeloid metaplasia * No ≥ grade 3 myelofibrosis * Atypical CML * Juvenile myelomonocytic leukemia * Other clonal hemopathies with an accepted poor prognosis * Multiple myeloma with chromosome 13 abnormalities and/or progression after prior autologous bone marrow transplantation (BMT) * Chronic lymphocytic leukemia, meeting 1 of the following criteria: * Primary refractory OR relapsed and refractory disease (less than partial remission) * Relapsed twice on or after prior chemotherapy * Lymphoma, meeting both of the following criteria: * Hodgkin's or non-Hodgkin's lymphoma in \> CR-1 OR failed primary induction * Chemosensitive disease, defined as \> 50% reduction in mass size after the most recent chemotherapy * Must meet ≥ 1 of the following criteria: * Over 45 years of age * Has undergone prior autologous or allogeneic BMT * Charlson\^ comorbidity score ≥ 2 * Must have a high degree of tumor control (salvage therapy allowed) * At high risk for treatment-related mortality with a myeloablative conditioning regimen * No massive splenomegaly * Patients may become eligible after splenectomy or radiotherapy to the spleen * No 5/6 or 6/6 HLA-matched related donor available * No well-matched (i.e., ≥ 9/10 HLA match by high-resolution typing) unrelated donor available PATIENT CHARACTERISTICS: Performance status * Not specified Life expectancy * Not specified Hematopoietic * See Disease Characteristics Hepatic * Bilirubin ≤ 2 times upper limit of normal (ULN) * Transaminases ≤ 4 times ULN (unless due to underlying disease) Renal * Creatinine clearance ≥ 50 mL/min Cardiovascular * Ejection fraction ≥ 30% Pulmonary * DCLO ≥ 35% Other * Negative pregnancy test * No uncontrolled viral, bacterial, or fungal infection * HIV negative PRIOR CONCURRENT THERAPY: Biologic therapy * See Disease Characteristics Chemotherapy * See Disease Characteristics Radiotherapy * See Disease Characteristics Other * At least 3 months since prior immunosuppressive therapy * At least 10 days since prior salvage therapy for patients not in at least morphologic or radiologic complete remission