This phase II trial studies how well donor atorvastatin treatment works in preventing severe graft-versus-host disease (GVHD) after nonmyeloablative peripheral blood stem cell (PBSC) transplant in patients with hematological malignancies. Giving low doses of chemotherapy, such as fludarabine phosphate, before a donor PBSC transplantation slows the growth of cancer cells and may also prevent the patient's immune system 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). Sometimes the transplanted cells from a donor can also cause an immune response against the body's normal cells (GVHD). Giving atorvastatin to the donor before transplant may prevent severe GVHD.