ASTX727 and FT-2102 in Treating IDH1-Mutated Recurrent/Refractory Myelodysplastic Syndrome or Acute Myeloid Leukemia

Inclusion Criteria: * Must voluntarily sign an informed consent document (ICF) * Morphologically confirmed diagnosis of MDS (inclusive of MDS/MPN) or AML in accordance with World Health Organization (WHO) diagnostic criteria * Phase Ib: Subjects may have * Relapsed/refractory AML or MDS or * Treatment naive AML * Phase II Expansion: Subjects may have * Relapsed/refractory AML or MDS or * Treatment naive AML or * Treatment naive MDS * For patients with MDS, must have a Revised International Prognostics Scoring System (IPSS-R) risk category of intermediate, high, or very high * Confirmed IDH1 R132 mutation * A bone marrow biopsy must be performed and tissue collected for entrance to the trial * Subjects must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0-2 * Life expectancy of at least 3 months in the assessment of the investigator * Recovery from the non-hematologic toxic effects of prior treatment to grade =\< 1, or baseline value according to National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) version (v)4.03 classification (excluding infertility, alopecia, or grade 1 neuropathy) * Must have adequate hepatic and renal function as demonstrated by the following: ALT (SGPT) and/or AST (SGOT) ≤ 3x upper limit of normal (ULN); Direct bilirubin ≤ 1.5 x ULN(or ≤ 2x ULN if due to Gilbert's disease); Serum creatinine of 1.5 x ULN or creatinine clearance of \> 50 mL/min (whichever is lower) * Baseline Fridericia's correction formula (QTcF) =\< 450 msec (average of the QTcF values of screening triplicate electrocardiography \[ECG\]swith approximately two-minute intervals ) except for those patients with a bundle branch block (BBB) * For fertile men and women, agreement to use effective contraceptive methods for the duration of study participation and 90 days after the last dose of study medication Exclusion Criteria: * Treatment naive patients who are suitable for and willing to receive intensive induction chemotherapy * Patients with active, uncontrolled infection. Patients with infection under active treatment and controlled with antibiotics are eligible * Concurrent condition that in the investigator's opinion would jeopardize compliance with the protocol * Known history of human immunodeficiency virus (HIV), or known active hepatitis A, B, or C infection (hepatitis B carriers with normal liver function test \[LFT\]s and undetectable viral loads are allowed) * Women who are pregnant or nursing * Organ transplant recipients other than bone marrow transplant * Autologous hematologic stem cell transplant within 3 months of study entry. Allogeneic hematologic stem cell transplant within 6 months. Grade II, or greater, active graft-versus- host disease * Use of an investigational drug within 21 days or 5 half-lives (whichever is shorter) prior to the first dose of FT-2102/ASTX727. For investigational drugs for which 5 half-lives is less than 21 days, a minimum of 10 days between termination of the investigational drug and administration of FT-2102/ASTX727 is required * Any major surgery, chemotherapy, or immunotherapy within the last 21 days (limited palliative radiation is allowed \>= 2 weeks); concurrent hydroxyurea is allowed if less than or equal to 2 grams daily * Ongoing immunosuppressive therapy including systemic corticosteroids (prednisone or equivalent =\< 20 mg daily allowed as clinically warranted). Patients are allowed to use topical or inhaled corticosteroids * Concurrent condition that in the investigator's opinion would jeopardize compliance with the protocol. * Patients unable to swallow oral medications, or patients with gastrointestinal conditions (e.g., malabsorption, resection, etc.) deemed by the Investigator to jeopardize intestinal absorption * Patients receiving intrathecal chemotherapy for active central nervous system (CNS) disease * Patients who have exhibited allergic reactions to a previously administered IDH1 inhibitor * Patients with acute promyelocytic leukemia (APL)