This phase II trial studies how well giving treosulfan together with fludarabine phosphate and total-body irradiation (TBI) works in treating patients with hematological cancer who are undergoing umbilical cord blood transplant (UCBT). Giving chemotherapy, such as treosulfan and fludarabine phosphate, and TBI before a donor UCBT helps stop the growth of cancer cells and helps stop the patient's immune system from rejecting the donor's stem cells. When the stem cells from a related or unrelated donor, that do not exactly match the patient's blood, 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 also make an immune response against the body's normal cells. Giving cyclosporine and mycophenolate mofetil after the transplant may stop this from happening.