Blasts Under 5 Percent of Bone Marrow Nucleated Cells

This phase II trial studies how well naive T-cell depletion works in preventing chronic graft-versus-host disease in children and young adults with blood cancers undergoing donor stem cell transplant. Sometimes the transplanted white blood cells from a donor attack the body's normal tissues (called graft versus host disease). Removing a particular type of T cell (naive T cells) from the donor cells before the transplant may stop this from happening.