 This clinical trial studies the use of reduced intensity chemotherapy and radiation therapy before donor stem cell transplant in treating patients with hematologic malignancies. Giving low doses of chemotherapy, such as cyclophosphamide and fludarabine phosphate, before a donor stem cell transplant may help stop the growth of cancer cells. It may also stop the patients immune system from rejecting the donors stem cells. The donated stem cells may replace the patients immune cells and help destroy any remaining cancer cells graft-versus-tumor effect. Reducing the intensity of the chemotherapy and radiation may also reduce the side effects of the donor stem cell transplant. 