 This phase II trial is studying the side effects and best dose of alemtuzumab when given together with fludarabine phosphate and total-body irradiation followed by cyclosporine and mycophenolate mofetil in treating patients who are undergoing a donor stem cell transplant for hematologic cancer. Giving low doses of chemotherapy, such as fludarabine phosphate, a monoclonal antibody, such as alemtuzumab, and radiation therapy before a donor stem cell transplant helps stop the growth of cancer cells. Giving chemotherapy or radiation therapy before or after transplant also stops the patients immune system from rejecting the donors bone marrow stem cells. The donated stem cells may replace the patients immune cells and help destroy any remaining cancer cells graft-versus-tumor effect. Sometimes the transplanted cells from a donor can also make an immune response against the bodys normal cells. Giving cyclosporine and mycophenolate mofetil after the transplant may stop this from happening. 