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 malignanc…