Omacetaxine and Venetoclax for the Treatment of Relapsed or Refractory Acute Myeloid Leukemia or Myelodysplastic Syndrome Harboring Mutant RUNX1

Inclusion Criteria: * Patients with a diagnosis of relapsed or refractory acute myeloid leukemia (AML) (or biphenotypic or bilineage leukemia including a myeloid component) or myelodysplastic syndrome * For myelodysplastic syndrome (MDS) patients, patients must have no response, progression, or relapse following at least 4 cycles of azacytidine or decitabine; and/or intolerance defined as grade \>= 3 drug-related toxicity precluding continued therapy * Age \>= 18 years * Subjects must have documented RUNX1 gene mutation * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Creatinine \< 2 unless related to the disease * Direct bilirubin \< 2x upper limit of normal (ULN) unless increase is due to Gilbert's disease or leukemic involvement * Aspartate aminotransferase (AST) and/or alanine aminotransferase (ALT) \< 3x ULN unless considered due to leukemic involvement * In the absence of rapidly proliferative disease, the interval from prior treatment to time of initiation will be at least 7 days for cytotoxic or non-cytotoxic (i.e. immunotherapy) agents. Oral hydroxyurea and/or cytarabine (up to 2 g/m\^2) for patients with rapidly proliferative disease is allowed before the start of study therapy, as needed, for clinical benefit and after discussion with the principal investigator (PI) * Male subjects must agree to refrain from unprotected sex and sperm donation from initial study drug administration until 90 days after the last dose of study drug * Willing and …