This phase II trial studies how well haploidentical donor hematopoietic stem cell transplant works in treating patients with hematologic malignancies. Giving 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. Giving an infusion of the donor's T cells (donor lymphocyte infusion) may replace the patient's immune cells and help destroy any remaining cancer cells. When the stem cells from a related donor, that closely matches the patient's blood, are infused into the patient they may help the patient's bone marrow make stem cells, red blood cells, white blood cells, and platelets.