Umbilical Cord Blood Transplantation From Unrelated Donors

This trial studies stem cell transplants using donated umbilical cord blood to treat blood cancers and rare immune or metabolic disorders in people who cannot find a closely matched bone marrow donor. **You may be eligible if...** - You have a blood cancer such as leukemia, lymphoma, or multiple myeloma that has come back or did not respond to standard treatment - You have a rare immune system disorder, bone marrow failure, or inherited metabolic disease that can be treated with a stem cell transplant - Your heart, lungs, kidneys, and liver are working well enough to handle the transplant - You are in reasonably good physical condition (able to carry out normal activity) **You may NOT be eligible if...** - A closely matched bone marrow donor (related or unrelated) is available and ready in time - You had a stem cell transplant using your own cells within the past 6 months - You are pregnant or breastfeeding - You have an active, uncontrolled infection - You are HIV positive Talk to your doctor to see if this trial is right for you.