Organ-Sparing Marrow-Targeted Irradiation Before Stem Cell Transplant in Treating Patients With High-Risk Hematologic Malignancies

Inclusion Criteria: * Patients with a diagnosis of acute myeloid leukemia (AML), acute lymphoblastic leukemia (ALL), or myelodysplastic syndromes (MDS) with fewer than 10% myeloblasts or lymphoblasts in the bone marrow and no blasts in the peripheral blood on morphologic analysis performed within 30 days of start of the conditioning regimen; if remission bone marrow is available beyond 30 days a new bone marrow evaluation is required to assess remission status * The diagnosis of AML, ALL, or MDS will be based on World Health Organization (WHO) criteria * Pre-transplant bone marrow sample must be evaluable for assessment of remission status (i.e. aspirate smear containing particles and/or evaluable bone marrow core biopsy) * Patients with leukemia infiltration in the central nervous system (CNS) are eligible if cerebrospinal fluid (CSF) cytospin is negative for myeloblasts or lymphoblasts at time of enrollment * If the patient has an intra-abdominal chloroma on presentation, and has a partial response or complete response to treatment (size reduction of chloroma and marrow blast \< 10%), the patient is eligible; however the chloroma must be included as part of the treatment target * For patients receiving treatment of their AML, MDS or ALL prior to transplantation: * Interval between the start of a cycle of conventional cytotoxic chemotherapy and the start of conditioning regimen must be at least 30 days * Interval between completing treatment with a hypomethylating agent or other non-cytotoxic chemotherapy and the start of conditioning regimen must be at least 10 days * Hematopoietic Cell Transplantation-Specific Comorbidity Index score (HCT-CI) =\< 4 for patients in Cohort 1 and \> 4 for Cohort 2 * Patient must be able to lie still in full body cast for 45 minutes * Must have a suitable donor defined as a sibling matched at 5/6 or 6/6 antigens (human leukocyte antigen \[HLA\]-A, B, and DRB1) or an unrelated volunteer matched at 7/8 or 8/8 HLA alleles (HLA-A, B, C, and DRB1) * Signed informed consent * DONOR: "High resolution" typing at HLA-A, B, C and DRB1 alleles * Single antigen mismatch for siblings and single allele mismatch for volunteer unrelated donors is acceptable * Donors must be \>= 17 years of age Exclusion Criteria: * Circulating peripheral blood myeloblasts or lymphoblasts on morphologic analysis from time of last treatment to time of enrollment * Prior allograft or prior autograft * Active CNS disease as identified by positive CSF cytospin at time of enrollment * Karnofsky performance score \< 70 * Symptomatic uncontrolled coronary artery disease or ejection fraction \< 40% * Total bilirubin \>= 2 x the upper limit of normal * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) \>= 3 x the upper limit of normal * Diffusion capacity of the lung for carbon monoxide (DLCO) \< 40% * Forced expiratory volume in one second (FEV1) \< 50% (corrected for hemoglobin) * Receiving supplementary continuous oxygen * Creatinine clearance \< 50 mL/min/1.73m\^2 * Patients with active uncontrolled bacterial, viral or fungal infections (undergoing appropriate treatment and with progression of clinical symptoms) * Patients seropositive for the human immunodeficiency virus (HIV) * Females who are pregnant or breastfeeding * Fertile men and women unwilling to use contraceptive techniques during and for 12 months following treatment * Patients who had prior radiation to more than 20% bone marrow containing areas or to any areas exceeding 2000 cGy * DONOR: * Donors will be excluded if they are an identical twin of the recipient * Females who are pregnant (positive serum beta human chorionic gonadotropin beta \[β HCG\]) or uninterruptible breastfeeding * HIV seropositive * Donors receiving experimental therapy or investigational agents unless approved by the protocol chair