RATIONALE: Giving low doses of chemotherapy, such as cyclophosphamide and fludarabine, total-body irradiation, and rituximab 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. The donated stem cells may replace the patient's immune cells 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 cyclosporine and mycophenolate mofetil after the transplant may stop this from happening.