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 that have been treated in the laboratory 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 tacrolimus before and after transplant may stop this from happening. PURPOSE: This phase I trial is studying the side effects and best dose of donor lymphocytes when given after alemtuzumab and combination chemotherapy in treating patients who are undergoing donor stem cell transplant for hematologic cancer.
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