RATIONALE: Drugs used in chemotherapy, such as fludarabine and cyclophosphamide, work in different ways to stop the growth of cancer cells, either by killing the cells or by stopping them from dividing. Radiation therapy uses high-energy x-rays to kill cancer cells. An umbilical cord blood transplant may be able to replace blood-forming cells that were destroyed by chemotherapy and radiation therapy. Sometimes the transplanted cells from a donor can make an immune response against the body's normal cells. Giving sirolimus and mycophenolate mofetil after the transplant may stop this from happening.
PURPOSE: This phase II trial is studying how well giving fludarabine and cyclophosphamide together with total-body irradiation followed by an umbilical cord blood transplant, sirolimus, and mycophenolate mofetil works in treating patients with hematologic cancer.