Docetaxel, Carboplatin, and Rucaparib Camsylate in Treating Patients With Metastatic Castration Resistant Prostate Cancer With Homologous Recombination DNA Repair Deficiency

Inclusion Criteria: * Signed informed consent form (ICF) providing agreement to adhere to the dosing schedule, report for all trial visits and authorization, use and release of health and research trial information * Histologically or cytologically confirmed adenocarcinoma of the prostate (excluding predominant small cell histology) * Ongoing gonadal androgen deprivation therapy with gonadotropin-releasing hormone (GnRH) analogues, antagonists or orchiectomy; patients who have not had an orchiectomy must be maintained on effective GnRH analogue/antagonist therapy * Castration resistant prostate cancer as defined by serum testosterone \< 50 ng/ml and PSA level of at least 2 ng/ml that has risen on at least 2 successive occasions at least 1 week apart * Presence of metastatic disease on bone or computed tomography (CT) scan * Evaluable disease progression by modified RECIST 1.1 (Response Evaluation Criteria in Solid Tumors) * Bone disease on bone scan * Prior therapy with sipuleucel-T, abiraterone, enzalutamide, docetaxel, and/or cabazitaxel; there is no limit to the number of prior treatment regimens in the castration resistant setting, so long as prior therapy does not include platinum chemotherapy or a PARP inhibitor; prior platinum chemotherapy in the hormone sensitive setting is permitted, so long as it has been at least 6 months since last dose * Eastern Cooperative Oncology Group (ECOG) performance status of =\< 1 * Life expectancy \>= 12 weeks * No prior malignancy is allowed except: * Adequately treated basal cell or squamous cell skin cancer or * In situ carcinoma of any site or * Other adequately treated malignancy for which the patient has been disease-free for at least one year (any prior chemotherapy is allowed) * Documented evidence of at least ONE or MORE of the following: \* Pathogenic mutation or inactivating alteration of a gene involved in homologous recombination repair in the tumor * Note, that if this alteration is identified in a circulating tumor deoxyribonucleic acid (ctDNA) assay, the variant-allele fraction must be \> 20% to indicate relevance to predominant tumor clone * Mutation in one or more other genes involved in homologous DNA recombination repair in the tumor may be included at investigator's discretion * Homologous recombination repair deficiency by genomic signature in the tumor by BROCA-HR, Foundation One or equivalent assay * Presence of pathogenic or likely pathogenic germline mutation/variant in BRCA2, BRCA1, ATM or PALB2 * Note: Germline mutations in other HR genes will be considered at investigator's discretion) * Absolute neutrophil count (ANC) \>= 1.5 x 10\^9/L (within 14 days of first dose of study drug) * Platelets \> 100 x 10\^9/L (within 14 days of first dose of study drug) * Hemoglobin \>= 9 g/dL (within 14 days of first dose of study drug) * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 3 x ULN; if liver metastases, then =\< 5 x ULN (within 14 days of first dose of study drug) * Bilirubin =\< 1.5 x ULN (\< 2 x ULN if hyperbilirubinemia is due to Gilbert's syndrome) (within 14 days of first dose of study drug) * Serum creatinine =\< 1.5 x ULN or estimated glomerular filtration rate (GFR) \>= 45 mL/min using the Cockcroft Gault formula (within 14 days of first dose of study drug) Exclusion Criteria: * Currently receiving active therapy for other neoplastic disorders * Symptomatic and/or untreated central nervous system (CNS) metastases; patients with asymptomatic previously treated CNS metastases are eligible provided they have been clinically stable for at least 4 weeks * Known human immunodeficiency virus (HIV) or acquired immunodeficiency syndrome (AIDS)-related illness, active or symptomatic viral hepatitis or chronic liver disease * Clinically significant heart disease as evidenced by myocardial infarction, or arterial thrombotic events in the past 6 months, severe or unstable angina, or New York Heart Association (NYHA) class II-IV heart disease or cardiac ejection fraction measurement of \< 35 % at baseline * Treatment with an investigational therapeutic drug within 30 days of cycle 1 * Prior therapy with a PARP inhibitor (e.g., olaparib, talazoparib, veliparib, niraparib, rucaparib) * Prior therapy with a platinum chemotherapy (e.g. cisplatin, carboplatin, oxaliplatin) in the castration resistant setting; (prior platinum chemotherapy in the hormone sensitive setting is permitted, so long as time since last dose is 6 months or greater) * Active, ongoing toxicity (Common Terminology Criteria for Adverse Events \[CTCAE\] grade 2 or higher) from prior therapy * Presence of dementia, psychiatric illness, and/or social situations limiting compliance with study requirements or understanding and/or giving of informed consent * Pre-existing duodenal stent and/ or any gastrointestinal disorder or defect that would, in the opinion of the Investigator, interfere with absorption of rucaparib * Any condition(s), medical or otherwise, which, in the opinion of the investigators, would jeopardize either the patient or the integrity of the data obtained