 This phase II trial studies the side effects and best dose of iodine I 131 monoclonal antibody BC8 when given together with fludarabine phosphate, total-body irradiation, and donor stem cell transplant followed by cyclosporine and mycophenolate mofetil in treating patients with acute myeloid leukemia or myelodysplastic syndrome that has spread to other places in the body and usually cannot be cured or controlled with treatment. Giving chemotherapy drugs, such as fludarabine phosphate, and total-body irradiation before a donor peripheral blood stem cell transplant helps stop the growth of cancer or abnormal cells and helps stop the patients immune system from rejecting the donors stem cells. Also, radiolabeled monoclonal antibodies, such as iodine I 131 monoclonal antibody BC8, can find cancer cells and carry cancer-killing substances to them without harming normal cells. When the healthy stem cells from a donor are infused into the patient they may help the patients 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 bodys normal cells. Giving fludarabine phosphate and total-body irradiation before the transplant together with cyclosporine and mycophenolate mofetil after the transplant may stop this from happening. Giving a radiolabeled monoclonal antibody together with donor stem cell transplant, cyclosporine, and mycophenolate mofetil may be an effective treatment for advanced acute myeloid leukemia or myelodysplastic syndromes. 