Allogeneic lymphocytes(Roswell Park Cancer Institute)

RATIONALE: Giving low doses of chemotherapy before a donor peripheral blood stem cell transplant helps stop the growth of cancer cells. It also stops the patient's immune system from rejecting the donor's stem cells. The donated stem cells may replace the patient's immune system 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 immunosuppressive therapy before or after the transplant may stop this from happening.
PURPOSE: This phase II trial is studying how well chemotherapy followed by donor peripheral stem cell transplant works in treating patients with hematologic cancer or aplastic anemia.