This phase II trial studies how well giving fludarabine phosphate, cyclophosphamide, tacrolimus, mycophenolate mofetil and total-body irradiation together with a donor bone marrow transplant works in treating patients with high-risk hematologic cancer. Giving low doses of chemotherapy, such as fludarabine phosphate and cyclophosphamide, and total-body irradiation before a donor bone marrow transplant helps stop the growth of cancer cells by stopping them from dividing or killing them. Giving cyclophosphamide after transplant may also stop the patient's immune system from rejecting the donor's bone marrow stem cells. The donated stem cells may replace the patient's immune system cells and help destroy any remaining cancer cells (graft-versus-tumor effect). Sometimes the transplanted cells from a donor can also make an immune response against the body's normal cells. Giving tacrolimus and mycophenolate mofetil after the transplant may stop this from happening