Umbilical Cord Blood T-Regulatory Cell Infusion Followed by Donor Umbilical Cord Blood Transplant in Treating Patients With High-Risk Leukemia or Other Hematologic Diseases

RATIONALE: Giving chemotherapy, such as fludarabine and cyclophosphamide, and total-body irradiation before a donor umbilical cord blood stem cell transplant helps stop the growth of cancer or abnormal 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. The donated stem cells may replace the patient's immune cells and help destroy any remaining cancer or abnormal cells (graft-versus-tumor effect). Giving an infusion of the donor's T-regulatory cells before the transplant may help increase this effect. Sometimes the transplanted cells from a donor can make an immune response against the body's normal cells. Giving cyclosporine and mycophenolate mofetil after the transplant may stop this from happening. PURPOSE: This phase I trial is studying the side effects and best dose of umbilical cord blood T-regulatory cell infusion followed by donor umbilical cord blood transplant in treating patients with high-risk leukemia or other hematologic diseases.