 This clinical trial studies the side effects and best dose of giving fludarabine and total-body irradiation TBI together followed by a donor stem cell transplant and cyclosporine and mycophenolate mofetil in treating human immunodeficiency virus HIV-positive patients with or without cancer. Giving low doses of chemotherapy, such as fludarabine, and TBI before a donor bone marrow or peripheral blood stem cell transplant helps stop the growth of cancer or abnormal cells and helps 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. Sometimes the transplanted cells from a donor can also make an immune response against the bodys normal cells. Giving cyclosporine CSP and mycophenolate mofetil MMF after the transplant may stop this from happening. 