Reduced-Intensity Busulfan and Fludarabine With or Without Antithymocyte Globulin Followed by Donor Stem Cell Transplant in Treating Patients With Hematologic Cancer or Other Disease

RATIONALE: Giving low doses of chemotherapy, such as busulfan and fludarabine, before a donor stem cell transplant helps stop the growth of cancer and abnormal cells. It also helps stop 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 or abnormal cells (graft-versus-tumor effect). Sometimes the transplanted cells from a donor can also make an immune response against the body's normal cells. Immunosuppressive therapy may improve bone marrow function and may be an effective treatment for hematologic cancer or other disease. PURPOSE: This clinical trial is studying the side effects and how well giving busulfan and fludarabine with or without antithymocyte globulin followed by donor stem cell transplant works in treating patients with hematologic cancer or other disease.