RATIONALE: Giving chemotherapy and total body irradiation before a donor bone marrow transplant or peripheral blood stem cell transplant helps stop the growth of cancer cells. It also helps stop the patient's immune system from rejecting the donor's stem cells. When the healthy stem cells from a donor are infused into the patient they may help the patient's bone marrow make stem cells, red blood cells, white blood cells, and platelets. Sometimes the transplanted cells from a donor can make an immune response against the body's normal cells. Giving antithymocyte globulin and removing the T cells from the donor cells before transplant may stop this from happening. PURPOSE: This phase I trial is studying the side effects and best dose of donor T cells and antithymocyte globulin when given together with chemotherapy and total-body irradiation in treating young patients who are undergoing T-cell depleted donor stem cell transplant for myelodysplastic syndrome, leukemia, bone marrow failure syndrome, or severe immunodeficiency disease.
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Engraftment at 4 weeks post bone marrow transplantation through 100 days
Timeframe: 100 days