This clinical trial studies fludarabine phosphate, low-dose total-body irradiation, and donor stem cell transplant followed by cyclosporine, mycophenolate mofetil, and donor lymphocyte infusion in treating patients with hematopoietic cancer. Giving low doses of chemotherapy, such as fludarabine phosphate, and total body irradiation (TBI) before a donor peripheral blood stem cell transplant helps stop the growth of cancer cells. It may also keep the patient's immune response 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. Sometimes the transplanted cells from a donor can also make an immune response against the body's normal cells. Giving cyclosporine and mycophenolate mofetil after the transplant may stop this from happening.