PLX51107 and Azacitidine in Treating Patients With Acute Myeloid Leukemia or Myelodysplastic Syndrome

Inclusion Criteria: * Diagnosis of * AML (World Health Organization \[WHO\] classification definition of \>= 20% blasts), or * MDS intermediate-2 score or with \> 10% blasts, to include: MDS, myeloproliferative neoplasm (MPN) with 10% blasts or more, or MDS/MPN 10% blasts or more * Patients who have received at least one prior therapy for AML or for MDS will be eligible. Any prior therapy for AML or MDS will be counted as a prior salvage * In the absence of rapidly progressing disease, the interval from prior treatment to time of initiation of protocol therapy will be at least 2 weeks for cytotoxic agents or at least 5 half-lives for cytotoxic/non-cytotoxic agents. The half-life for the therapy in question will be based on published pharmacokinetic literature (abstracts, manuscripts, investigator brochures, or drug-administration manuals) and will be documented in the protocol eligibility document. The use of chemotherapeutic or anti-leukemic agents is not permitted during the study with the following exceptions: * Intrathecal (IT) therapy for patients with controlled central nervous system (CNS) leukemia at the discretion of the principal investigator (PI). Controlled CNS leukemia is defined by the absence of active clinical signs of CNS disease and no evidence of CNS leukemia on the most recent 2 simultaneous cerebrospinal fluid (CSF) evaluations * Use of one dose of cytarabine (up to 2 g/m\^2) or hydroxyurea for patients with rapidly proliferative disease is allowed before the start of study therapy and for the first four weeks on therapy. These medications will be recorded in the case-report form. * Eastern Cooperative Oncology Group (ECOG) performance status 0-2 * Measured or calculated creatinine clearance \>= 60 mL/min (unless considered due to leukemia) * Total bilirubin \< 1.8 mg/dL (unless increase is due to hemolysis, congenital disorder, or leukemia) * Transaminases (serum glutamate pyruvate transaminase \[SGPT\]) \< 2.5 x upper limit of normal (ULN) (unless considered due to leukemia) * Potassium levels should be within institutional normal limits (unless considered due to leukemia) * Magnesium levels should be within institutional normal limits (unless considered due to leukemia) * Calcium (normalized for albumin) levels should be within institutional normal limits (unless considered due to leukemia) * Ability to take oral medication * Ability to understand and provide signed informed consent prior to any study-related procedures and to comply with all study requirements * Baseline left ventricular ejection fraction by echocardiogram (ECHO) or multigated acquisition scan (MUGA) \>= 50% * Women of childbearing potential (WOCBP) must have a negative serum or urine pregnancy test within 7 days. Men must agree not to father a child and agree to use a condom if his partner is of child bearing potential * WOCBP must use appropriate method(s) of contraception. WOCBP should use an adequate method to avoid pregnancy until after the last dose of investigational drug. Women who are not of childbearing potential (i.e., who are postmenopausal or surgically sterile) as well as men with azoospermia do not require contraception Exclusion Criteria: * Patients with known significant impairment of gastrointestinal (GI) function or GI disease that may significantly alter the absorption of PLX51107 * Patients with any other known concurrent severe and/or uncontrolled medical condition including but not limited to diabetes, cardiovascular disease including hypertension, renal disease, or active uncontrolled infection, which could compromise participation in the study. Patients on active antineoplastic or radiation therapy for a concurrent malignancy at the time of screening. Maintenance therapy, hormonal therapy, or steroid therapy for well-controlled malignancy is allowed * Patients with known positive human immunodeficiency virus (HIV), hepatitis B or C infection by serology, with the exception of those with an undetectable viral load within 3 months. (HIV testing and hepatitis B or C testing is not required prior to study entry). Subjects with serologic evidence of prior vaccination to hepatitis B virus (HBV) (i.e., hepatitis B virus surface antigen negative \[HBs Ag-\], and hepatitis B surface antibody positive \[HBs+\]) may participate * Patients with advanced malignant hepatic tumors * Patients with known hypersensitivity to AZA or mannitol * Women who are pregnant or are breast-feeding * Patients who receive strong CYP3A4 and CYP2C8 inhibitors or inducers or CYP3A4 substrate drugs with a narrow therapeutic range, taken within 14 days or 5 drug half-lives, whichever is longer, before start of study drug * Patients who have received anti-cancer therapy within 14 days (or 5 half-lives) with all toxicities resolved to grade 1 or less. No immune therapy or other biologic therapy (other monoclonal antibodies or antibody-drug conjugates \[ADCs\]) within 28 days of cycle 1 day 1