Total Marrow and Lymphoid Irradiation in Combination With Fludarabine and Melphalan as Conditioning for Allogeneic Peripheral Blood Stem Cell Hematopoietic Cell Transplant in Older Patients With Refractory and Relapsed Acute Myeloid Leukemia and High-risk Myelodysplastic Syndrome

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative * Assent, when appropriate, will be obtained per institutional guidelines * Agreement to allow the use of archival tissue from diagnostic tumor biopsies * If unavailable, exceptions may be granted with study principal investigator (PI) approval * Age: ≥ 50 years (no upper age limit) * Note: Patients ≥ 18 years and \< 50 years are also included if they are not candidates for myeloablative conditioning regimens due to comorbidities or active disease * Karnofsky or Lansky performance status ≥ 70 * Eligible patients will have a histopathological confirmed diagnosis of hematologic malignancy in one of the following categories: * Acute myeloid leukemia (AML): * Patients with de novo or secondary disease in unfavorable risk group including poor risk cytogenetics according to National Comprehensive Cancer Network (NCCN) guidelines for AML i.e., monosomal karyotype, -5,5q-,-7,7q-,11q23-non t(9;11), inv (3), t(3;3), t(6;9), t(9;22) and complex karyotypes (≥ 3 unrelated abnormalities), or all patient in intermediate risk groups * Patients with active disease: * Morphologically * Minimal residual disease (MRD) testing (MRD+ through flow cytometry, cytogenetics, or molecular assays) * Myelodysplastic syndrome/chronic myelomonocytic leukemia (CMML) (MDS) with ≥ 10% blast * Patients must have an human leukocyte antigen (HLA) (A, B, C, and DRB1) identical sibling or a 8/8 (A, B, C, and DR) allele matched unrelated donor who is willing to donate primed blood stem cells * Serum direct bilirubin ≤ 2.0 x upper limit of normal (ULN) (unless has Gilbert's disease) (within 35 days prior to day 1 of protocol therapy unless otherwise stated) * Aspartate aminotransferase (AST) ≤ 2.5 x ULN (within 35 days prior to day 1 of protocol therapy unless otherwise stated) * Alanine aminotransferase (ALT) ≤ 2.5 x ULN (within 35 days prior to day 1 of protocol therapy unless otherwise stated) * Creatinine clearance of ≥ 60 mL/min per 24 hour urine test or the Cockcroft-Gault formula (within 35 days prior to day 1 of protocol therapy unless otherwise stated) * Left ventricular ejection fraction (LVEF) ≥ 50% * Note: To be performed within 35 days prior to day 1 of protocol therapy * If able to perform pulmonary function tests: Forced expiratory volume in 1 second (FEV1), forced vital capacity (FVC) and DLCO (diffusion capacity) ≥ 50% of predicted (corrected for hemoglobin) * Note: To be performed within 35 days prior to day 1 of protocol therapy * If unable to perform pulmonary function tests: Oxygen (O2) saturation \> 92% on room air * Note: To be performed within 35 days prior to day 1 of protocol therapy * Seronegative for HIV antigen (Ag)/antibody (Ab) combo, hepatitis C virus (HCV), active hepatitis B virus (HBV) (surface antigen negative) (within 35 days prior to day 1 of protocol therapy unless otherwise stated) * If seropositive for HIV, HCV or HBV, nucleic acid quantitation must be performed. Viral load must be undetectable * HIV-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial * Meets institutional and federal requirements for infectious disease titer requirements * Note: Infectious disease testing to be performed within 28 days prior to day 1 of protocol therapy * Women of childbearing potential (WOCBP): Negative urine or serum pregnancy test (within 35 days prior to day 1 of protocol therapy unless otherwise stated) * If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Agreement by females and males of childbearing potential to use an effective method of birth control or abstain from heterosexual activity for the course of the study through at least 6 months after the last dose of protocol therapy * Childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only) Exclusion Criteria: * Allogeneic stem cell transplant or autologous HCT within 1 year prior to day 1 of protocol therapy * Chemotherapy, radiation therapy, biological therapy, immunotherapy within 14 days of day 1 of protocol therapy * Note: Low dose chemotherapy or maintenance chemotherapy given within 7 days of planned study enrollment is permitted. These include hydroxyurea, 6-meraptopurine, oral methotrexate, vincristine, oral etoposide, and tyrosine kinase inhibitors (TKIs). TKIs can also be given up to 3-5 days before conditioning regimen * More than three previous lines of intensive chemotherapy, where the regimen intent was to induce remission * Co-enrollment in other clinical trials involving post-HCT maintenance interventions or any study with potential to affect disease-free survival is not allowed * History of allergic reactions attributed to compounds of similar chemical or biologic composition to study agent * Clinically significant uncontrolled illness * Active infection not responding to antibiotics * Other active malignancy. Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial * Females only: Pregnant or breastfeeding * Any other condition that would, in the investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns with clinical study procedures * Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)