Donor Stem Cell Transplant in Treating Patients With Relapsed Hematologic Malignancies or Secondary Myelodysplasia Previously Treated With High-Dose Chemotherapy and Autologous Stem Cell Transplant

RATIONALE: Giving chemotherapy, such as busulfan and fludarabine phosphate, before a peripheral blood stem cell transplant helps stop the growth of cancer cells. It may also stop the patient's immune system from rejecting the donor's stem cells. Sometimes the transplanted cells from a donor can make an immune response against the body's normal cells. Giving methotrexate, tacrolimus, and antithymocyte globulin before and after the transplant may stop this from happening. Once the donated stem cells begin working, the patient's immune system may see the remaining cancer cells as not belonging in the patient's body and destroy them (called graft-versus-tumor effect). Giving an infusion of the donor's white blood cells (donor lymphocyte infusion) may boost this effect. PURPOSE: This phase II trial is studying how well donor stem cell transplant works in treating patients with relapsed hematologic malignancies or secondary myelodysplasia previously treated with high-dose chemotherapy and autologous stem cell transplant .