Donor Umbilical Cord Blood Transplant in Treating Patients With Advanced Hematologic Cancer

RATIONALE: Giving chemotherapy, such as fludarabine, busulfan, and etoposide, before a donor umbilical cord blood stem cell transplant helps stop the growth of cancer 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 antithymocyte globulin before transplant and tacrolimus and prednisone after transplant may stop this from happening. PURPOSE: This phase I trial is studying how well donor umbilical cord blood transplant works in treating patients with advanced hematologic cancer.