Treosulfan-Based Versus Clofarabine-Based Conditioning Before Donor Hematopoietic Stem Cell Transplant for the Treatment of Myelodysplastic Syndromes or Acute Myeloid Leukemia

Inclusion Criteria: * Age \>= 18 years and =\< 75 years * Diagnosis of MDS-EB or AML: must have \< 5% marrow blasts (by morphology and/or flow cytometry) at time of transplant * Karnofsky performance score (KPS) \>= 60% on pre-HCT evaluation * Able to give informed consent * Patients with previous autologous or allogeneic HCT may enroll * DONOR: Human leukocyte antigen (HLA)-identical related donors or unrelated donors matched for HLA-A, B, C, DRB1, and DQB1 as defined by high resolution deoxyribonucleic acid (DNA) typing; mismatch for only one HLA allele at class I is allowed * DONOR: Donors able to undergo peripheral blood stem cell collection. Only granulocyte colony-stimulating factor (G-CSF) mobilized peripheral blood stem cell (PBSC) will be permitted as an hematopoietic stem cell (HSC) source on this protocol Exclusion Criteria: * Presence of circulating blasts (in the blood) detected by standard pathology for patients with AML * Presence of \>= 5% circulating leukemic blasts (in the blood) detected by standard pathology for patients with MDS-EB * Patients with promyelocytic AML * Organ dysfunction * Cardiac: Ejection fraction \< 35% (or, if unable to obtain ejection fraction, shortening fraction of \< 26%) or cardiac insufficiency requiring treatment or symptomatic coronary artery disease. Patients with a shortening fraction \< 26% may be enrolled if approved by a cardiologist * Pulmonary: * Diffusion capacity of the lung for carbon monoxide (DLCO) \< 40%, total lung capacity (TLC) \< 40%, forced expiratory volume in 1 second (FEV1) \< 40% and/or receiving supplementary continuous oxygen. When pulmonary function test (PFT)s cannot be obtained, the 6-minute walk test (6 minute walk functional test \[6MWT\], also known as exercise oximetry) will be used: Any patient with oxygen saturation on room air of \< 89% during a 6MWT will be excluded * The principal investigator (PI) must approve enrollment of all patients with pulmonary nodules * Renal: Serum creatinine should be within normal limits as specified by Standard Practice guidelines. For subjects with serum creatinine \> upper limit of normal, a 24-hour creatinine clearance will be performed and should be equal to or more than the lower limit of normal * Hepatic: Patients with clinical or laboratory evidence of liver disease will be evaluated for the cause of liver disease, its clinical severity in terms of liver function, and the degree of portal hypertension. Patients will be excluded if they are found to have fulminant liver failure, cirrhosis of the liver with evidence of portal hypertension, alcoholic hepatitis, esophageal varices, a history of bleeding esophageal varices, hepatic encephalopathy, uncorrectable hepatic synthetic dysfunction evidenced by prolongation of the prothrombin time, ascites related to portal hypertension, bridging fibrosis, bacterial or fungal liver abscess, biliary obstruction, chronic viral hepatitis with total serum bilirubin \> 3 mg/dL, or symptomatic biliary disease * With active infectious disease requiring deferral of conditioning, as recommended by an infectious disease specialist * Fungal infections with radiological progression after receipt of amphotericin B or active triazole for greater than 1 month * With human immunodeficiency virus (HIV)-positivity or active infectious hepatitis because of possible risk of lethal infection when treated with immunosuppressive therapy * With central nervous system (CNS) leukemia at the time of treatment * Patients with active non-hematologic malignancies (except non-melanoma skin cancers) or those with non-hematologic malignancies (except non-melanoma skin cancers) who have been rendered with no evidence of disease but have a greater than 20% chance of having disease recurrence within five years. This exclusion does not apply to patients with non-hematologic malignancies that do not require therapy * With life expectancy severely limited by diseases other than malignancy * Fertile men and women unwilling to used contraceptive techniques during treatment and for 12 months following * Women who are pregnant or lactating * With known hypersensitivity to treosulfan, fludarabine, or clofarabine * The use of non-Food and Drug Administration (FDA) approved investigational drugs would not be allowed within 4 weeks of the initiation of conditioning (day -6 for both arms) * Unable to give informed consent * Patients suitable for and willing to receive a standard high intensity preparative regimen * DONOR: Donor (or centers) who will exclusively donate marrow * DONOR: Donors who are HIV-positive and/or, medical conditions that would result in increased risk for G-CSF mobilization and harvest of PBSC * DONOR: Donors are excluded when preexisting immunoreactivity is identified that would jeopardize donor hematopoietic cell engraftment. This determination is based on the standard practice of the individual institution. The recommended procedure for patients with 10 of 10 HLA allele level (phenotypic) match is to obtain a panel reactive antibody (PRA) screens to class I and class II antigens for all patients before HCT. If the PRA shows \> 10% activity, then flow cytometric or B and T cell cytotoxic cross matches should be obtained. The donor should be excluded if any of the cytotoxic cross match assays are positive. For those patients with an HLA Class I allele mismatch, flow cytometric or B and T cell cytotoxic cross matches should be obtained regardless of the PRA results. A positive anti-donor cytotoxic cross match is an absolute donor exclusion * DONOR: Donor is excluded if a patient is homozygous in the graft-rejection vector against the donor's mismatched HLA class I allele