RATIONALE: Giving low doses of chemotherapy and radiation therapy before a donor umbilical cord blood stem cell transplant helps stop the growth of cancer cells. It also stops the patient's immune system from rejecting the donor's stem cells when they do not exactly match the patient's blood. The donated stem cells may replace the patient's immune system and help destroy any remaining cancer cells (graft-versus-tumor effect). Sometimes the transplanted cells from a donor can also make an immune response against the body's normal cells. Giving antithymocyte globulin before transplant and cyclosporine and mycophenolate mofetil after transplant may stop this from happening.