RATIONALE: Giving chemotherapy drugs, such as fludarabine and cyclophosphamide, and total-body irradiation before a donor umbilical cord blood stem cell transplant helps stop the growth of cancer cells and prepares the patient's bone marrow for the stem cells. When the healthy stem cells from a donor are infused into the patient they may help the patient's bone marrow make stem cells, red blood cells, white blood cells, and platelets. Sometimes the transplanted cells from a donor can make an immune response against the body's normal cells. Giving cyclosporine and mycophenolate mofetil may stop this from happening.
PURPOSE: This phase II trial is studying how well giving fludarabine and cyclophosphamide together with total-body irradiation works in treating patients who are undergoing an umbilical cord blood transplant for hematologic cancer.