Brief Summary: This phase I/II trial studies the side effects and best dose of donor natural killer cells when given together with donor stem cell transplant and to see how well they work in treating patients with myeloid malignancies that are likely to come back or spread. Giving chemotherapy, such as busulfan and fludarabine phosphate, before a donor peripheral blood stem cell transplant helps stop the growth of cancer cells. It may also stop the patient's immune system from rejecting the donor's stem cells. When the healthy stem cells and natural killer 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.

Detailed Description: PRIMARY OBJECTIVES: I. Assess the safety of infusing ex vivo expanded natural killer (NK) cells in patients receiving busulfan-fludarabine phosphate (fludarabine) with an allogeneic human leukocyte antigen (HLA) matched hematopoietic transplantation for myeloid malignancies. Two sources of NK cells could be studied, depending on what donor source is available: cells from the HLA matched related donor or cells from an unrelated cord blood unit. II. For each source of NK cells: the maximum tolerated cell dose; the phenotype and function of the ex vivo expanded NK cells and their survival in vivo; the rate of engraftment, graft-vs.-host disease (GVHD), immune reconstitution, relapse rates and survival for patients receiving this regimen will be determined. OUTLINE: This is a phase I, dose-escalation study of NK cells followed by a phase II study. Patients receive fludarabine phosphate intravenously (IV) over 1 hour and busulfan IV over 3 hours on days -13 to -10. Patients then receive allogeneic CD56-positive CD3-negative natural killer cells IV over 1 hour on day -8. Patients also receive aldesleukin subcutaneously (SC) once daily (QD) on days -8 to -4. Patients then undergo allogeneic peripheral blood stem cell (PBSC) transplant on day 0.