Study of ASTX727 Plus Talazoparib in Patients With Triple Negative or Hormone Resistant/HER2-negative Metastatic Breast Cancer

Inclusion Criteria: 1. ≥ 18 years old at the time of informed consent 2. Ability to provide written informed consent and HIPAA authorization 3. Locally recurrent (not amenable to local therapy with curative intent) or metastatic breast cancer 1. Patients with triple negative breast cancer must have received at least one prior chemotherapy regimen for metastatic disease. 2. Patients with hormone-positive, HER2-negative disease must have received treatment with and progressed on at least one prior endocrine therapy including a CDK4/6 inhibitor in the metastatic setting. 4. Measurable or evaluable disease based on RECIST 1.1 criteria. 5. Only subjects who have disease amenable to biopsy will be asked to consent to serial tumor biopsies. Consent for biopsy is not required for participation. a. NOTE: If no amendable disease is present at the time of biopsy, subjects may continue participation in the study and further study specific biopsies will not be required. 6. Eastern Cooperative Oncology Group Performance Status 0 or 1 7. Patients with treated, asymptomatic central nervous system (CNS) disease may participate if the patient is \> 4 weeks from completion of CNS therapy (radiation and/or surgery), is clinically stable at the time of study entry, and is receiving a stable or decreasing dose of corticosteroid therapy. Brain MRI or head CT is required at screening for patients with known brain metastases. 8. Adequate organ function as indicated by: 1. Total bilirubin \</= ULN (upper limit of normal) (except in patients with documented Gilbert's disease, who must have a total bilirubin \</= 3.0 mg/dL) 2. Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) \</= 3.0 x ULN (\</= 1.5-3.0 x baseline if baseline is abnormal) 3. Calculated creatinine clearance of \>/= 60 mL/min using the Cockcroft-Gault formula 4. Absolute neutrophil count (ANC) \>/= 1.5 K/mm3 5. Platelets \>/= 100 K/mm3 6. Hemoglobin (Hgb) \>/= 9.0 g/dL 9. Women of childbearing potential must have a negative pregnancy test within 14 days of protocol registration. Women are considered to have childbearing potential (regardless of sexual orientation, having undergone a tubal ligation, or remaining celibate by choice) unless they meet one of the following criteria: 1. Has undergone a hysterectomy or bilateral oophorectomy; or 2. Has been naturally amenorrheic for at least 24 consecutive months. 10. Women of childbearing potential and men must agree to use effective contraception throughout the study and for 7 months after the last study treatment. Note: Acceptable methods of birth control include abstinence, partner with previous vasectomy, placement of an intrauterine device (IUD), condom with spermicidal foam/gel/film/cream/suppository, diaphragm or cervical vault cap, or hormonal birth control (pills or injections). Exclusion Criteria: 1. Prior treatment with decitabine, guadecitabine or other known DNA Methyltransferase inhibitors (DNMTis) 2. Prior treatment with talazoparib or other known PARPi (poly(ADP-ribose polymeras inhibitor) 3. Known deleterious breast cancer susceptibility gene (BRCA) mutation. Patients with BRCA variants of unknown significance (VUS) or who have not had germline genetic testing may participate. 4. Active or symptomatic CNS disease 5. Patients with HER2+ disease * HER2 will be considered positive if scored 3+ by immunohistochemistry (IHC) or 2+ by IHC associated with a fluorescence in situ hybridization (FISH) ratio of \> 2.0 or \> 6 total HER2 gene copies per cell. 6. Patients with active malignancy other than breast cancer. Patients with prior malignancies without recurrence after standard treatment will not be excluded 7. Chemotherapy within 3 weeks of registration 8. Radiation therapy within 2 weeks of registration 9. Hormone therapy within 2 weeks of registration 10. Patients requiring ongoing therapy with strong P-gp inhibitors