Laboratory-Treated Donor Bone Marrow in Treating Patients Who Are Undergoing a Donor Bone Marrow Transplant for Hematologic Cancer

RATIONALE: Giving chemotherapy and total-body irradiation before a donor bone marrow transplant or peripheral blood stem cell transplant helps stop the growth of cancer and abnormal cells and helps stop the patient's immune system from rejecting the donor's stem cells. When certain stem 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. Sometimes the transplanted cells from a donor can make an immune response against the body's normal cells. Removing the T cells from the donor cells before transplant may stop this from happening. PURPOSE: This randomized phase III trial is studying donor bone marrow that is treated in the laboratory using two different devices to compare how well they work in treating patients who are undergoing a donor bone marrow transplant for hematologic cancer.