Busulfan and Fludarabine Before Donor Stem Cell Transplant in Treating Patients With Hematologic Cancer

DISEASE CHARACTERISTICS: * Diagnosis of 1 of the following hematopoietic disorders: * Chronic myelogenous leukemia (CML), meeting 1 of the following criteria: * Chronic phase disease failing imatinib mesylate therapy * Progressive disease OR failed to achieve a major cytogenetic response at 1 year after initiation of therapy * Accelerated phase disease, meeting 1 of the following criteria: * Failed to achieve complete cytogenetic remission at 1 year after initiation of therapy * Failed to achieve any cytogenetic response at 3 or 6 months during therapy * Progressive disease, demonstrated by worsening cytogenetic response in 2 consecutive analyses separated by 4 weeks * Blast crisis with \< 10% blasts in bone marrow within 6 weeks of transplantation * Acute myeloid leukemia (AML), meeting 1 of the following criteria: * In second or greater remission * In first remission with poor prognosis cytogenetics \[-5, -5q, -7, -7q and ≥ 2 cytogenetic abnormalities, t(6,9), t(9,11), or Philadelphia chromosome\] * In hematologic remission but with persistent cytogenetic abnormalities * Primary refractory AML with \< 10% blasts in bone marrow within 6 weeks of transplantation * Myelodysplasia with \< 20% blasts in bone marrow within 6 weeks of transplantation and meeting 1 of the following criteria: * Advanced disease (International Prognostic Scoring System \[IPSS\] score intermediate-1, intermediate-2, or high risk) * Myelodysplastic syndromes (MDS) with progression to AML * Treatment-related AML * Acute lymphocytic leukemia (ALL), meeting 1 of the following criteria: * In second or greater remission * In first remission with high-risk cytogenetics \[Philadelphia chromosome; t(4,11); and -7\] * Primary refractory ALL with \< 10% blasts in the bone marrow * Severe aplastic anemia that has failed immunosuppressive therapy * Non-Hodgkin's lymphoma, meeting 1 of the following criteria: * In second or greater remission * Relapsed disease in a patient not eligible for autologous stem cell transplantation * Lymphoproliferative disease (e.g., chronic lymphocytic leukemia or Waldenstrom's macroglobulinemia), meeting 1 of the following criteria: * In second or greater remission * Relapsed disease in a patient not eligible for autologous stem cell transplantation * Multiple myeloma, meeting 1 of the following criteria: * Stage II or III disease in first or greater relapse * Refractory disease * Newly diagnosed disease with chromosome 13 abnormalities * Advanced myeloproliferative disease, meeting 1 of the following criteria: * Myelofibrosis requiring \> 2 units of packed red blood cells each month * Essential thrombocythemia or polycythemia rubra vera that has progressed to AML * Failed prior AML therapy * No active, uncontrolled CNS leukemia * Not eligible for autologous or mini-allogeneic transplantation * No fully matched or single-antigen mismatched sibling donor available * HLA-matched unrelated donor available * HLA typed at HLA-A, -B, -C, -DRB1 and/or -DQB1 by high-resolution techniques * For patients without HLA identical donors, mismatches at DQ (i.e., 8/8 match) and 1 additional mismatch at the allele level at HLA-A, -B, -C, or -DRB1 (i.e., 7/8 molecular match) allowed PATIENT CHARACTERISTICS: * ECOG performance status 0-2 * Creatinine \< 2.0 mg/dL * Pulmonary diffusing capacity \> 40% of predicted * Cardiac ejection fraction \> 40% by MUGA or echocardiography * No active liver disease * Bilirubin ≤ 2.0 mg/dL * Alkaline phosphatase \< 3 times upper limit of normal (ULN) * AST \< 3 times ULN * Hepatitis C or active hepatitis B (HBV) allowed provided a liver biopsy is performed and ≤ grade 2 inflammation is present * Patients with active HBV viral replication must receive antiviral therapy * HIV negative * No ongoing active infection * Not pregnant or nursing * Negative pregnancy test PRIOR CONCURRENT THERAPY: * See Disease Characteristics * More than 3 weeks since prior chemotherapy except for hydroxyurea or imatinib mesylate * More than 3 months since prior interferon