Carboplatin Chemotherapy Before Surgery for People With High-Risk Prostate Cancer and an Inherited BRCA1 or BRCA2 Gene Mutation

Inclusion Criteria: Participant must have histologic diagnosis of prostate adenocarcinoma Participant must have high or very high-risk disease defined by at least one of the following: cT3a - cT4x Grade group 4 or 5 (Gleason sum 8-10) PSA > 20 ng/mL prior to registration Participant must have documented evidence of germline mutation (pathogenic/likely pathogenic variant) in BRCA2 or BRCA1 through testing in a Clinical Laboratory Improvement Act (CLIA)-certified lab NOTE: Local lab report is sufficient for eligibility Participant may have initiated gonadotrophin releasing hormone (gnRH) agonist, gnRH antagonist, oral anti-androgen (e.g. bicalutamide, nilutamide, flutamide), or other agent intended to treat prostate cancer prior to registration. The effectiveness of the current depot of such treatment must not extend beyond 1 month after study registration. Agents listed above cannot be started after participant registration Participant must be >= 18 years old Participant must have Zubrod performance status of 0-2 Participant must have a complete medical history and physical exam within 28 days prior to registration Absolute neutrophil count >= 1.5 x 10^3/uL (within 28 days prior to registration) Platelets >= 100 x 10^3/uL (within 28 days prior to registration) Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =< 3 x institutional upper limit of normal (ULN) (within 28 days prior to registration) Participant must have a serum creatinine =< the institutional upper limit of normal (IULN) OR measured OR calculated creatinine clearance >= 50 mL/min using the following Cockcroft-Gault Formula. This specimen must have been drawn and processed within 28 days prior to registration Participant must have adequate cardiac function. Participants with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, must have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification within 28 days prior to registration. To be eligible for this trial, participants must be class 2B or better Participant with known human immunodeficiency virus (HIV)-infection must be receiving anti-retroviral therapy and have an undetectable viral load test within 6 months prior to registration Participant with history of chronic hepatitis B virus (HBV) infection must have undetectable HBV viral load on suppressive therapy within in 28 days prior to registration Participant with a history of hepatitis C virus (HCV) infection must have been treated and cured. For participants with HCV infection who are currently on treatment must have an undetectable HCV viral load within in 28 days prior to registration Participants who are of reproductive potential must have agreed to use an effective contraceptive method with details provided as a part of the consent process. A person who has semen likely to contain sperm is considered to be of "reproductive potential." In addition to routine contraceptive methods, "effective contraception" also includes refraining from sexual activity that might result in pregnancy and surgery intended to prevent pregnancy (or with a side-effect of pregnancy prevention) including vasectomy with testing showing no sperm in the semen Prior to registration, participant must have had a urologic consult and be deemed a surgical candidate with known sites of disease deemed by the urologist to be potentially resectable Participants must be offered the opportunity to participate in specimen banking. With participant consent, specimens must be collected and submitted via the Southwest Oncology Group (SWOG) Specimen Tracking System NOTE: As a part of the OPEN registration process the treating institution's identity is provided in order to ensure that the current (within 365 days) date of institutional review board approval for this study has been entered in the system Participants must be informed of the investigational nature of this study and must sign and give informed consent in accordance with institutional and federal guidelines For participants with impaired decision-making capabilities, legally authorized representatives may sign and give informed consent on behalf of study participants in accordance with applicable federal, local, and Central Institutional Review Board (CIRB) regulations As part of the registration process the treating institution's identity is provided in order to ensure that the current (within 365 days) date of institutional review board approval for this study has been entered in the system Exclusion Criteria: Participant must not have evidence of distant metastatic disease by conventional imaging within 90 days prior to registration NOTE: cN1 detected only by PSMA-PET is permitted if urologist deems sites of disease to be potentially completely resectable Participant must not have received prior radiation therapy (RT) to the pelvic region Participant must not have a prior or concurrent malignancy whose natural history or treatment (in the opinion of the treating physician) has the potential to interfere with the safety or efficacy assessment of protocol treatment