This clinical trial studies reduced-intensity conditioning before donor stem cell transplant in treating patients with high-risk hematologic malignancies. Giving low-doses of chemotherapy and total-body irradiation before a donor stem cell transplant helps stop the growth of cancer cells. It may also 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 cells (donor lymphocyte infusion) after the transplant may help increase this effect.