Talazoparib for Cohesin-Mutated AML and MDS With Excess Blasts

Inclusion Criteria: * Participants must be considered ineligible to receive intensive chemotherapy by treating investigator and must have a diagnosis of one of the following: * Secondary AML (can be untreated secondary AML if previously treated for MDS, MDS/MPN, or any MPN with any anti-leukemic therapy; but cannot be recommended to receive any available approved AML therapy) * Relapsed or refractory AML or relapsed/refractory AML without available approved AML therapy including transplantation or intensive chemotherapy or targetable lesion such as FLT3 or IDH1/IDH2 * Relapsed or Refractory MDS with a minimum of at least 4 cycles of decitabine or 6 cycles of azacitidine or sooner if they experience intolerance/progression/relapse while on HMA-based therapy. * Persistent MDS/AML disease despite receiving at least 2 cycles of hypomethylating agent and venetoclax * Previously untreated higher risk MDS by IPSS-R (\>3.5) who require treatment per treating investigator. Exceptions: Patients recommended for immediate transplant and have a donor ready or patients recommend for intensive chemotherapy * Participants must have measurable disease defined as 5% or more blasts (blood or bone marrow). * Age 18 years and older. * ECOG performance status ≤2 (see Appendix A) * Participants must have normal organ function as defined below: * total bilirubin ≤ 2.5 × institutional upper limit of normal (unless considered to be secondary to leukemia) * AST(SGOT)/ALT(SGPT) ≤ 2.5 × institutional upper limit of normal (unless considered to be secondary to leukemia) * creatinine clearance ≥ 60 mL/min/1.73 m2 * Documented pathogenic mutation in cohesin complex including a mutation in STAG2, SMC1A, RAD21, PDS5B, or SMC3 gene from a CLIA-approved test (local testing allowed; will be centrally confirmed). Patient must have a minimum VAF of 5%. Historical results from (up to 3 months prior to study registration) allowed for treatment start on study if no recent disease-modifying agent was received since testing. * The effects of Talazoparib on the developing human fetus are unknown. For this reason and because PARP inhibitor agents are suspected to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of the study participation, and 4 months after completion of Talazoparib administration. * For women of child bearing potential only, must have a negative urine or serum pregnancy test. * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Participants receiving any leukemia-directed chemotherapy within 2 weeks prior to study registration or those who have not recovered from adverse events (to at least grade 1 with exception of alopecia) due to chemotherapy administered more than 2 weeks earlier. Exceptions: hydroxyurea and prior palliative radiotherapy is permitted if completed within 5 days prior to study registration and patient has no clinically significant toxicities such as mucositis or esophagitis. * No prior PARP inhibitor for any indication. * No limitations to prior MDS/AML therapy including HMA (azacitidine or decitabine). If a patient is post allogeneic hematopoietic stem cell transplant, he/she must be \> 2 months from day of donor cell infusion to date of study registration. They must be off immunosuppression therapy for at least 14 days prior to registration (topical steroids are permitted). * Participants who are receiving any other investigational agents. * Participants with known CNS leukemia. * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements or compromise safety assessment, in the judgement of the investigator. * Pregnant women are excluded from this study because Talazoparib is a PARP inhibitor agent with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with Talazoparib, breastfeeding should be discontinued if the mother is treated with Talazoparib. These potential risks may also apply to other agents used in this study. * Patient has known active HIV, HCV or HBV. * Patients with prior malignancy are eligible however patient must either be in remission from prior malignancy OR have inactive (note: meaning they do not require treatment) and asymptomatic disease. Maintenance therapy such as hormone therapy is allowed