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Cyclophosphamide, Fludarabine Phosphate, and Total-Body Irradiation with or without Anti-Thymocyte Globulin before Donor Umbilical Cord Blood Transplant in Treating Patients with Hematologic Cancer

Trial Status: administratively complete

This phase II trial studies the side effects of cyclophosphamide, fludarabine phosphate, and total-body irradiation with or without anti-thymocyte globulin before donor umbilical cord blood transplant and to see how well they work in treating patients with hematologic (blood) cancer. Giving chemotherapy and total-body irradiation before donor umbilical cord blood transplant helps stop the growth of cells in the bone marrow, including normal blood-forming cells (stem cells) and 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 (called graft-versus-host disease). Giving sirolimus and mycophenolate mofetil before and after the transplant may stop this from happening.