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