Tosedostat and Cytarabine or Azacitidine in Treating Older Participants With Acute Myeloid Leukemia or High Risk Myelodysplastic Syndrome

Inclusion Criteria: * Signed, informed consent must be obtained prior to any study specific procedures * For the phase I portion of the study patients should have failed any number of prior therapies, which should include at least the following: * Patients with MDS should have failed prior therapy with a hypomethylating agent and/or with lenalidomide * Patients with AML should have failed any prior induction therapy or have relapsed after prior therapy * Patients with MDS who received therapy with a hypomethylating agent and progress to AML are eligible at the time of diagnosis of AML regardless of any prior therapy for AML * Patients with any of the eligible diagnoses who have received no prior therapy are eligible if not candidates to receive standard therapy or if they refuse standard chemotherapy * For the phase II portion of the study, only patients who are previously untreated for AML. 1. Patients with history of MDS who received therapy for MDS and progressed to AML are eligible at the time of diagnosis of AML. Only induction chemotherapy administered for AML will be considered for considerations of eligibility regarding prior therapy. Patients who received therapy for MDS before transforming to AML (e.g., with hypomethylating agents or lenalidomide) are eligible * Eastern Cooperative Oncology Group (ECOG) performance status of 0-1 * Women of child-bearing potential (i.e., women who are pre-menopausal or not surgically sterile) must use acceptable contraceptive methods (abstinence, intrauterine device \[IUD\], oral contraceptive or double barrier device) while on study and must continue to do so for 3 months after stopping study drug, and must have a negative urine or serum pregnancy test within 2 weeks prior to beginning treatment on this trial. Sexually active men must also use acceptable contraceptive methods for the duration of time on study. Pregnant and nursing patients are excluded because the effects of tosedostat on a fetus or nursing child are unknown * Patients must have been off chemotherapy for 2 weeks prior to entering this study, unless there is evidence of rapidly progressive disease, and must have recovered from the toxic effects of that therapy to at least grade 1. Use of hydroxyurea for patients with rapidly proliferative disease is allowed before the start of study therapy and for the first four weeks on therapy * Serum creatinine =\< 2.0 mg/dl * Total bilirubin =\< 1.5 x the upper limit of normal unless considered due to Gilbert's syndrome * Alanine aminotransferase (ALT), or aspartate aminotransferase (AST) =\< 3 x the upper limit of normal * Left ventricular ejection fraction (LVEF) \>= 50% within 28 days prior to first dose of study drug administration * Patient is able to comply with all study procedures including study drug administration, visits and tests * For patients with history of anthracycline exposure or coronary artery disease co-management by cardiology to optimize cardioprotective medications will be required prior to tosedostat initiation Exclusion Criteria: * Uncontrolled intercurrent illness including, but not limited to uncontrolled infection, symptomatic congestive heart failure (New York Heart Association class III or IV), or psychiatric illness/social situations that would limit compliance with study requirements * Active heart disease including myocardial infarction within previous 6 months, symptomatic coronary artery disease, clinically significant arrhythmias not controlled by medication, atrial fibrillation (whether active or known past history), uncontrolled angina, or uncontrolled congestive heart failure (New York Heart Association class III or IV) * Recent exposure to cardiotoxic agents (including anthracyclines) within 3 months of enrollment. Subjects with troponin-I and brain natriuretic peptide (BNP) levels above upper limit of normal (ULN) are excluded * Patients with acute promyelocytic leukemia (APL) (FAB type M3) or chronic myelogenous leukemia (CML) in blast crisis * Significant gastrointestinal disorders that may interfere with absorption of tosedostat * Patients who have received a stem cell transplant in the past * Patients who can receive an allogeneic stem cell transplant within 4 weeks * Use of concomitant drugs that prolong QT/corrected QT (QTc) interval are prohibited with the exception of antibiotics, antifungals, and other antimicrobials that are used as standard of care to prevent or treat infections and other such drugs that are considered absolutely essential for the care of the patient, but only if clinically indicated and must be fully documented