T-Cell Depletion, Donor Hematopoietic Stem Cell Transplant (HSCT), and T-Cell Infusions in Treating Patients With Hematologic Cancer or Other Diseases

RATIONALE: Giving chemotherapy and total-body irradiation before a donor 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 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. Giving an infusion of the donor's T cells (donor lymphocyte infusion) after the transplant may help destroy any remaining cancer cells (graft-versus-tumor effect). PURPOSE: This phase II trial is studying T-cell depletion in donor stem cell transplant followed by delayed T cell infusions in treating patients with hematologic cancer or other disease.