Allogeneic Bone Marrow Transplantation Using Less Intensive Therapy

OBJECTIVES: * Determine if a nonmyeloablative regimen comprising cyclophosphamide, fludarabine, and radiotherapy followed by cyclosporine and mycophenolate mofetil provides a prompt and durable donor engraftment in patients with hematologic malignancies or kidney cancer who are undergoing allogeneic stem cell transplantation. * Determine the safety of this nonmyeloablative transplantation regimen in these patients. * Determine the risk of graft-versus-host-disease in patients treated with this regimen. * Determine the antineoplastic potency of nonmyeloablative stem cell transplantation in patients treated with this regimen. * Determine the effect of lower doses of daily fludarabine on treatment-related mortality (TRM) OUTLINE: Patients are stratified according to risk (standard vs high). * Preparative regimen\*: Patients receive cyclophosphamide intravenously (IV) over 2 hours on day -6 and fludarabine IV over 1 hour on days -6 to -2. Patients undergo total body irradiation on day -1. Some patients also receive anti-thymocyte globulin (ATG)\*\* IV every 12 hours on days -6 to -4. Patients who receive ATG\* include the following: * Related donor recipients who have not received combination chemotherapy within the past 6 months * Unrelated donor recipients who have not received combination chemotherapy within the past 3 months * Unrelated donor recipients who have received only 1 induction course for the treatment of acute lymphoblastic leukemia (ALL), acute myeloid leukemia (AML), myelodysplastic syndromes (MDS), or blastic phase chronic myelogenous leukemia (CML) NOTE: \*\*Patients who underwent prior autologous stem cell transplantation in the past year do not receive ATG. * Allogeneic peripheral blood stem cell transplantation (PBSCT): Patients undergo allogeneic PBSCT on day 0. * Graft-versus-host-disease prophylaxis: Patients receive cyclosporine IV over 2 hours beginning on day -3 and continuing until at least day 100. Patients also receive mycophenolate mofetil IV or orally twice daily on days -3 to 30. * Donor lymphocyte infusion (DLI): Patients without active GVHD but deteriorating donor chimerism may receive DLI IV over 2 hours. After completion of study treatment, patients are followed periodically for 2 years. PROJECTED ACCRUAL: A total of 300 patients will be accrued for this study.