NK Cells in Cord Blood Transplantation

This phase I trial studies the side effects and best way to give natural killer cells and donor umbilical cord blood transplant in treating patients with hematological malignancies. Giving chemotherapy with or without total body irradiation before a donor umbilical cord blood transplant helps stop the growth of cancer cells. It may also stop the patient's immune system from rejecting the donor's stem cells. When the healthy stem cells and natural killer cells from a donor are infused into the patient they may help the patient's bone marrow make stem cells, red blood cells, white blood cells, and platelets.