Alemtuzumab, Fludarabine Phosphate, and Total-Body Irradiation Followed by Cyclosporine and Mycophenolate Mofetil in Treating Patients Who Are Undergoing Donor Stem Cell Transplant for Hematologic Cancer

Inclusion Criteria: * The patient must be not eligible for conventional transplants and must have disease expected to be stable for at least 100 days without chemotherapy * Patients with hematologic malignancies treatable with HCT will be included: * Aggressive non-Hodgkin lymphomas (NHLs) and other histologies such as diffuse large B-cell NHL: not eligible for autologous HCT, not eligible for conventional myeloablative HCT, or after failed autologous HCT; * Low grade NHL: with \< 6 month duration of complete response (CR) between courses of conventional therapy; * Mantle cell NHL: may be treated in first CR; * Chronic lymphocytic leukemia (CLL): must have failed 2 lines of conventional therapy and must be refractory to fludarabine; this includes patients who fail to have a complete or partial response after therapy with a regimen containing fludarabine (or another nucleoside analog\] or experience disease relapse within 12 months after completing therapy with a regimen containing fludarabine \[or another nucleoside analog); * Hodgkin's disease (HD): must have received and failed frontline therapy and have failed or were not eligible for autologous transplant; * Multiple myeloma (MM): must have received prior chemotherapy or failed autografting; following a planned autologous transplant \[tandem\] is allowed; * Acute myeloid leukemia (AML): must have \< 5% marrow blasts at the time of transplant; * Acute lymphocytic leukemia (ALL): must have \< 5% marrow bla…