This phase I/II trial studies how well cytokine-treated veto cells work in treating patients with hematologic malignancies following stem cell transplant. Giving chemotherapy and total-body irradiation before a stem cell transplant helps stop the growth of cells in the bone marrow, including normal blood-forming cells (stem cells) and cancer cells. When the healthy 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. Cytokine-treated veto cells may help the transplanted donor cells to develop and grow in recipients without causing graft-versus-host-disease (GVHD - when transplanted donor tissue attacks the tissues of the recipient's body).