T regulatory cells(University of Minnesota Masonic Cancer Center)

RATIONALE: Giving chemotherapy, such as fludarabine and cyclophosphamide, and total-body irradiation before a donor umbilical cord blood transplant helps stop 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). Giving an infusion of the donor's T-regulatory cells after the transplant may decrease this effect. Sometimes the transplanted cells from a donor can also make an immune response against the body's normal cells. However, the donor immune system may also react against the recipient's tissues (graft-versus-host disease).
PURPOSE: This phase I trial is studying the side effects and best dose of donor T-regulatory cells after an umbilical cord blood transplant in treating patients with advanced hematologic cancer or other disorder.