Talazoparib With Androgen Deprivation Therapy and Abiraterone for the Treatment of Castration Sensitive Prostate Cancer

Inclusion Criteria: * All patients must have a histologically or cytologically proven diagnosis of adenocarcinoma of the prostate. (Note: Gleason score not required if biopsy of metastasis was used to make the histologic diagnosis) * All patients must have metastatic disease: either soft tissue and/or bony metastases prior to initiation of androgen. Measurable disease is not required * Baseline imaging must have been performed within 42 days before or 14 days after initiating luteinizing hormone releasing hormones (LHRH) therapy. All disease must be assessed and documented on the Baseline Tumor Assessment Form * Patients may have started on LHRH therapy for metastatic prostate cancer provided this was initiated no longer than 60 days prior to registration * Patients may have received neoadjuvant and/or adjuvant LHRH therapy during definitive treatment or salvage radiation; if so at least 12 months must have elapsed from the last LHRH injection and baseline testosterone must be \> 150 ng/dL * No restriction on bicalutamide used for flare prevention or combined therapy however bicalutamide must be stopped at registration * Patients must have a Karnofsky performance status of 60 - 100 * Men of reproductive potential and those who are surgically sterilized (i.e., vasectomy) must agree to practice effective barrier contraception or agree to abstain from intercourse while receiving treatment on this study and for at least 4 months after protocol treatment ends * Bilirubin =\< 2 x institutional upper limit of normal (ULN) (obtained within 28 days prior to registration) * Serum glutamic-oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) and serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) =\< 2.5 x institutional ULN, or =\< 5 x institutional ULN if liver metastases are present (obtained within 28 days prior to registration) * Calculated creatinine clearance \>= 30 mL/min using a serum creatinine obtained within 28 days prior to registration * Leukocytes \>= 3,000/mcL (obtained within 28 days prior to registration) * Absolute neutrophil count (ANC) \>= 1,500/mcL (obtained within 28 days prior to registration) * Hemoglobin \>= 9 g/dL (obtained within 28 days prior to registration) * Platelets \>= 100,000/mcL (obtained within 28 days prior to registration) * All subjects must have the ability to understand and the willingness to sign a written informed consent * Patients may have received prior androgen deprivation therapy (ADT) -neoadjuvant and/or adjuvant, or in conjunction with salvage radiation - but it must not have lasted for more than 36 months. Single or combination therapy allowed. At least 6 months must have elapsed since completion of androgen deprivation therapy in the neoadjuvant and/or adjuvant setting, and serum testosterone must be \> 150 ng/mL within 28 days prior to registration. Note: Serum testosterone assessment is required for eligibility for only those with prior treatment with ADT * Patients who have already started on LHRH therapy are eligible, provided no more than 60 days have elapsed from LHRH injection (or surgical castration) for metastatic prostate cancer prior to registration. The start date of medical castration is considered the day the patient first received an injection of a LHRH agonist/antagonist (or orchiectomy), not an oral antiandrogen. Subjects may not already be taking abiraterone, enzalutamide, apalutamide or other intensification agent during this time - bicalutamide is permitted * Patients may have received palliative radiotherapy for symptomatic bone or visceral metastasis, provided they have recovered from all side effects at the time of registration * Patients may have received prior surgery. For all major surgeries, at least 14days must have elapsed since completion and patient must have recovered from all major side effects of surgery per investigator's assessment * Patients may have received or plan to receive concurrent bone targeting agents that do not have an effect on prostate specific antigen (PSA) (e.g. denosumab or bisphosphonate) Exclusion Criteria: * Patients must not have received prior and/or must not have any plans for receiving concomitant therapy with ketoconazole, aminoglutethimide, or enzalutamide (MDV3100). Concurrent megestrol for hot flashes is allowed * Patients must not have received any prior cytotoxic chemotherapy for metastatic prostate cancer * Prior cytotoxic chemotherapy with curative intent in the neoadjuvant or adjuvant setting may be allowed at the discretion of the principal investigator. At least 2 years must have elapsed since completion of cytotoxic chemotherapy in the neoadjuvant and/or adjuvant setting * Patients with known brain metastases are not eligible. Brain imaging studies are not required for eligibility if the patient has no neurologic signs or symptoms suggestive of brain metastasis. But, if brain imaging studies are performed, they must be negative for disease * Patients must not have New York Heart Association class III or IV heart failure at the time of screening. Patients must not have any thromboembolic event, unstable angina pectoris, myocardial infarction, or serious uncontrolled cardiac arrhythmia within 6 months prior to registration * Patients must not have uncontrolled hypertension (defined as blood pressure \> 160 mmHg systolic and \> 90 mmHg diastolic at 2 separate measurements no more than 60 minutes apart) despite appropriate medical therapy. Note: Patients may be rescreened after adjustments of antihypertensive medications * Patients must not be known to have human immunodeficiency virus (HIV) infection, active chronic hepatitis B or C, life-threatening illness unrelated to cancer, or any serious medical or psychiatric illness that could, in the investigator's opinion, potentially interfere with participation in this study * Patients with a known history of primary and secondary adrenal insufficiency are not eligible * History of allergic reactions attributed to compounds of similar chemical or biologic composition to any of the study drugs * Patients may not be receiving any other investigational agents, or concurrent biological, chemotherapy, or radiation therapy. Previous experimental therapy must have been completed at least 28 days prior to registration * Patients must not have known gastrointestinal (GI) disease or GI procedure that could interfere with the GI absorption or tolerance of any of the study drugs, including difficulty swallowing oral medications * No other prior malignancy is allowed except for the following: adequately treated basal cell or squamous cell skin cancer, adequately treated stage I or II cancer from which the patient is currently in complete remission, or any other cancer from which the patient has been disease-free for 5 years