NK Cell Based Non-Myeloablative Transplantation in Acute Myeloid Diseases

Inclusion Criteria: * Acute myeloid leukemia (AML) or myelodysplastic syndrome (MDS) RAEB-1 or RAEB-2 fitting within one of the following disease groups: * Primary induction failure (PIF): Patients who have not achieved a complete remission (CR) after two induction cycles of cytotoxic therapy (i.e. 7+ 3, MEC, FLAG, etc.) and having ≤ 10,000 absolute circulating blasts measured at least 21 days from prior therapy. Hydroxyurea may be used to control blasts count. Demethylating agents do not count as induction therapy; however early re-induction therapy based on residual disease on a day 14 BM will count as a 2nd cycle * Relapsed Disease with low disease burden (AML or MDS with ≤ 10,000 absolute circulating blasts. No re-induction attempts are required, but a maximum of 2 reinduction attempts are allowed to be eligible. * CR3 or greater: This will include CRp defined as CR without platelet recovery to 100,000/mcL. * CR1 or CR2 with high risk features: Includes therapy induced, prior MDS or MPD, high risk cytogenetic or molecular phenotype with no available donor (sibling or unrelated adult) Patients with known prior central nervous system (CNS) involvement are eligible provided that it has been treated and CSF is clear for at least 2 weeks prior to enrollment. CNS therapy (chemotherapy or radiation) should continue as medically indicated during the study treatment. * Available related HLA-haploidentical adult donor by at least Class I serologic typing at the A\&B locus * Karnofsky score \> 50% * Adequate organ function within 28 days of study registration defined as: * Hepatic: AST ≤ 3 x upper limit of institutional normal, total bilirubin ≤ 2.0 mg/dl * Renal: estimated glomerular filtration rate (GFR) ≥ 50 mL/min/1.73m\^2 * Pulmonary: Oxygen saturation ≥ 90% on room air and DLCOcor ≥ 40% * Cardiac: Ejection Fraction ≥ 35% and no uncontrolled angina, severe uncontrolled ventricular or arterial arrhythmias, or any evidence of acute ischemia or active conduction system abnormalities (rate controlled atrial fibrillation is not an exclusion) * Able to be off prednisone or other immunosuppressive medications for at least 3 days prior to NK cell infusion (except for those prescribed as part of the study) * Women of child bearing potential must have a negative pregnancy test within 28 days prior to study registration and agree to use adequate birth control during study treatment * Voluntary written consent Exclusion Criteria: * Biphenotypic leukemia * Allogeneic transplant for AML within previous 6 months * New or progressive pulmonary infiltrates on screening chest x-ray or chest CT scan that has not been evaluated with bronchoscopy, if feasible. Infiltrates attributed to infection must be stable/improving (with associated clinical improvement) after 1 week of appropriate therapy (4 weeks for presumed or documented fungal infections). * Uncontrolled bacterial, fungal or viral infections including HIV - chronic asymptomatic viral hepatitis is allowed * Known hypersensitivity to any of the study agents * Received any investigational drugs within the 14 days before 1st dose of fludarabine * Requires agents other than hydroxyurea to control blast count Donor Selection: * Related donor (sibling, parent, offspring, parent or offspring of an HLA identical sibling) 12-75 years of age. (It is recognized individual institutions may have differing donor age guidelines. This is acceptable as long as no donor is younger than 12 years or older than 75 years). * Body weight of at least 40 kilograms * In general good health as determined by the medical provider * HLA-haploidentical donor/recipient match by at least Class I serologic typing at the A\&B locus * Able and willing to have up to 4 separate apheresis collections * Not pregnant * Voluntary written consent