AlloHCT From Matched Unrelated Donors in Pts w/ Advanced Hematologic Malignancies & Disorders

RATIONALE: Giving chemotherapy with or without total-body irradiation before a donor umbilical cord blood transplant helps stop the growth of cancer or abnormal cells. It also helps stop the patient's immune system from rejecting the donor's stem cells. When the 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 before and after transplant may stop this from happening. PURPOSE: This clinical trial is studying how well four different chemotherapy regimens given with or without total-body irradiation before umbilical cord blood transplant work in treating patients with relapsed or refractory hematologic cancer.