Inclusion Criteria:  Participants must have histologically or cytologically confirmed diagnosis adenocarcinoma of the prostate. Prostate cancer must be metastatic as confirmed by CT, PET scan, and/or bone scan. Prior biopsy of metastatic lesion (bone, lymph node, or visceral metastasis) with sufficient tissue for molecular analysis, or consent for a fresh biopsy for molecular analysis Participants must have tested negative for homologous recombination (HR) mutations (including known deleterious mutations in BRCA1, BRCA2, or ATM) on a blood-based or tissue-based assay History of bilateral orchiectomies or ongoing GnRH agonist or antagonist Castration-resistant disease based on progression per Prostate Cancer Working Group 2.21 Prior treatment for metastatic prostate cancer with docetaxel and either abiraterone acetate or enzalutamide, OR ineligible for or declines treatment with docetaxel, abiraterone acetate, or enzalutamide. Adequate renal function with a serum creatinine ≤ 2.0 mg/dL or an estimated or calculated creatinine clearance of > 50 mL/min (calculated using the formula of Cockcroft and Gault) Adequate hepatic function with total bilirubin ≤ 1.5x the upper limit of normal (ULN) and ALT and AST less than 3x the ULN. Adequate hematological function with ANC ≥ 1500/mm3, hemoglobin ≥ 9.0 g/dL, and platelet count ≥ 100,000/mm3 Age ≥ 18 years ECOG performance status of 0 or 1 Ability to understand and the willingness to sign a written informed consent document  Patients/participants with female partners of childbearing potential are eligible to participate if they agree to ONE of the following for the duration of the study:  Are abstinent from penile-vaginal intercourse as their usual and preferred lifestyle (abstinent on a long-term and persistent basis) and agree to remain abstinent for duration of the study. Agree to use a male condom and have their partner use a contraceptive method with a failure rate of <1% per year (intrauterine device or hormonal implant). Patients/participants must refrain from donating sperm for the duration of the study. Patients/participants with a pregnant or breastfeeding partner must agree to remain abstinent from penile-vaginal intercourse or use a male condom during each episode of penile penetration for the duration of the study.  Exclusion Criteria:  Participants who have received more than two prior chemotherapy regimens for metastatic castration-resistant prostate cancer. Participants who have any previous treatment with PARP inhibitors Participants who are receiving any other investigational agents. Participants who have received radiation therapy within 2 weeks or radionuclide treatment within 6 weeks prior to registration on this study Participants with known brain metastases should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. History of allergic reactions attributed to compounds of similar chemical or biologic composition to telaglenastat or talazoparib Concurrent use of moderate or strong CYP3A4 inducers or inhibitors, which could affect talazoparib plasma concentrations 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. Patients known to be positive for Human Immunodeficiency Virus (HIV), Hepatitis B, or Hepatitis C.