A Study of Talazoparib With or Without Enzalutamide in People With Prostate Cancer Who Have Previously Received Abiraterone Acetate or Darolutamide

Inclusion Criteria • Willing and able to provide, or have a legally authorized representative provide, written informed consent and privacy authorization for the release of personal health information. A signed informed consent must be obtained before screening procedures are performed. NOTE: Privacy authorization may be either included in the informed consent or obtained separately. * Participants ≥ 18 years of age. * Are willing to be randomized into either study arm and adhere to the study protocol. * Ability to swallow study capsules and/or tablets whole. * Are willing to remain on study treatment and to continue undergoing study imaging despite PSA progression unless clinically deteriorating. * Histological or cytological proof of predominant adenocarcinoma of the prostate. * Presence of a pathogenic homologous recombination repair mutation in at least one of the following genes: BRCA1, BRCA2, ATM (limited to 15% of enrolled participants), CDK12, CHEK2, PALB2, MLH1, NBN, ATR, FANCA, MRE11A, RAD51C. Assessment of HRR mutation status by germline or somatic testing. All testing must be per Clinical Laboratory Improvement Amendments (CLIA)-certified assay and may have occurred at any time prior to or at screening (not required to be completed within the screening window). * Metastatic castration-resistant prostate cancer (mCRPC) as demonstrated by one or both of the following: * Metastatic disease documented by conventional imaging: computed tomography (CT)/magnetic resonance imaging (MRI) chest/abdomen/pelvis and bone scan are required to be performed, but metastases do not need to be seen on both modalities. Measurable disease is not required. * Unequivocal prostate-specific membrane antigen (PSMA) positron emission tomography (PET) only defined metastatic disease with negative conventional imaging. PSMA PET imaging is not required to be performed, but may be used to document metastases when relevant. * Progressed either via a minimum of 2 rising PSA levels with a minimun of a 1-week interval between each determination or via radiographic progression by any form of imaging while receiving either abiraterone acetate with prednisone for mHSPC or locally advanced disease, OR darolutamide for mHSPC, locally advanced disease, or non-metastatic castration-resistant disease. * Progressive disease at start of treatment and in the setting of medical or surgical castration as defined by 1 or more of the following 4 criteria: * PSA progression defined as 2 rising PSA levels, above an initial reference value, taken with a minimum of a 1-week interval. If PSA rise is the only indication of progression at start of study treatment, a minimum PSA of 1.0 ng/mL is required and all measured PSA values have to be considered to make a determination of progression. * Soft tissue disease progression as defined by RECIST 1.1. * Bone disease progression defined by PCWG3 with 2 or more new metastatic bone lesions on a whole-body radionuclide bone scan. * Appearance of newly identified, convincingly positive lesion(s) consistent with metastatic prostate cancer on PSMA PET. * Surgically or medically castrated, with testosterone levels of \<50 ng/dL. If the participant is medically castrated, continuous dosing with a gonadotropin-releasing hormone agonist or antagonist must be demonstrated by testosterone level of \<50 ng/dL and planned to continue throughout study participation. * Eastern Cooperative Oncology Group (ECOG) status of ≤2 (Appendix A: Performance Status Criteria). * Normal organ function with acceptable initial laboratory values within 35 days of treatment start: * Absolute neutrophil count ≥ 1,500/µl * Hemoglobin ≥ 9g/dl * Platelet count ≥ 100,000/µl * Creatinine ≤ 1.5 x the institutional upper limit of normal (ULN) * Potassium ≥ 3.5 mmol/L (within institutional normal range) * Bilirubin ≤ 1.3 x ULN (unless documented Gilbert's disease) * Serum glutamic oxaloacetic transaminase/aspartate transaminase (AST) ≤ 2.5 x ULN * Serum glutamic pyruvic transaminase/ alanine transaminase (ALT) ≤ 2.5 x ULN * Participants must agree to use a medically acceptable method of birth control (e.g., spermicide in conjunction with a barrier such as a condom) or sexual abstinence for the duration of the study, including 4 months after the last dose of study drug. Sperm donation is prohibited during the study and for 4 months after the last dose of study drug. Female partners must use hormonal or barrier contraception unless postmenopausal or abstinent. Exclusion Criteria * Any other active malignancy at time of first dose of study treatment or diagnosis of another malignancy within 2 years prior to first dose of study treatment that requires active treatment, except for locally curable cancers that have been apparently cured, such as basal or squamous cell skin cancer or superficial bladder cancer. * Prior treatment for metastatic CRPC with an ARPI for ≥ 12 weeks. * Prior treatment for non-metastatic CRPC with abiraterone acetate with prednisone, enzalutamide, or apalutamide for ≥ 12 weeks. * Participants who received chemotherapy for castration-sensitive prostate cancer are still eligible provided chemotherapy was completed ≥ 28 days prior to start of study treatment. * Participants who received PLUVICTO® for castration-sensitive prostate cancer are still eligible provided treatment was completed ≥ 42 days prior to start of study treatment. * Use of investigational agents for the treatment of prostate cancer ≤ 28 days of start of study treatment. * Prior treatment with a PARP inhibitor. * Concurrent treatment with crizotinib. * Prior platinum-based chemotherapy for the treatment of prostate cancer. * Current or planned use of potent P-gp inhibitors within 7 days prior to randomization. The P-gp inhibitors include: amiodarone, carvedilol, clarithromycin, cobicistat, dronedarone, erythromycin, glecaprevir/pibrentasvir, indinavir, itraconazole, ketoconazole, lapatinib, lopinavir, propaf