• Male \>= 18 years of age

• Histological confirmation of adenocarcinoma of the prostate

• Qualifying deleterious SPOP mutation detected on any archival genomic assay (tissue and/or liquid biopsy) is acceptable for study inclusion. Qualifying mutation(s) of SPOP include any genomic change predicted to be deleterious or suspected deleterious. SPOP status must be established prior to involvement on the trial

• Evidence of metastatic castration-resistant prostate cancer, defined as at least one (1) documented metastatic lesion on either bone scan or CT scan. Bone only disease is acceptable for enrollment. Non-bone metastatic lesions must be measurable by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 criteria. Subjects whose disease spread is limited to regional pelvic lymph nodes or local recurrence (e.g. bladder, rectum) are not eligible

• Radiographic or PSA progression while on androgen deprivation therapy (or after bilateral orchiectomy) AND at least one prior AR-targeted therapy (abiraterone acetate, enzalutamide, apalutamide, darolutamide or investigational AR-targeted agents). PSA progression is a PSA increase that is \>= 25% and \>= 2 ng/mL above the nadir, and which is confirmed by a second value (minimum 1 week interval between tests). For radiographic progression of soft tissue lesions, modified RECIST 1.1 criteria will be used to qualify entry. For radiographic progression of bony disease, two new lesions must be seen as per PCWG3 criteria. No confirmatory scan of bone progression is required prior to study entry

• A maximum of two lines of prior taxane (docetaxel and/or cabazitaxel) chemotherapy will be allowed, but are not required

• Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1 or 2

• Surgically or medically castrated, with serum testosterone levels of =\< 50 ng/dL (1.73 nM). For patients currently being treated with luteinizing hormone-releasing hormone (LHRH) analogs (ie, patients who have not undergone an orchiectomy), therapy must be continued throughout the study

• Absolute neutrophil count (ANC) \>= 1500/mm\^3 (within 14 days prior to registration)

• Platelet count \>= 100,000/mm\^3 (within 14 days prior to registration)

• Hemoglobin \>= 10 g/dL independent of transfusion within 14 days

• Total bilirubin =\< 1.5 x upper limit of normal (ULN) (In subjects with Gilbert's syndrome, if total bilirubin is \> 1.5 x ULN, measure direct and indirect bilirubin, and if direct bilirubin is =\< 1.5 x ULN, subject may be eligible as determined by the medical monitor) (within 14 days prior to registration)

• Alanine aminotransferase (ALT) =\< 3 x ULN (within 14 days prior to registration)

• Aspartate transaminase (AST) =\< 3 x ULN (within 14 days prior to registration)

• Calculated creatinine clearance \>= 45 ml/min using the Cockcroft-Gault formula (within 14 days prior to registration)

• Male patients who are committed to undertaking the following measures for the duration of the study and after the last dose of CJNJ-67652000 (niraparib/abiraterone acetate fixed-dose combination) for the time period specified:

‣ Use a condom during sex while being treated and for 120 days after the last dose of CJNJ-67652000 (niraparib/abiraterone acetate fixed-dose combination)

⁃ Do not make semen donations during treatment and for 120 days after the last dose of CJNJ-67652000 (niraparib/abiraterone acetate fixed-dose combination)

⁃ Those with female partners of childbearing potential may be enrolled if they are:

• Documented to be surgically sterile (ie, vasectomy);

∙ Committed to practicing true abstinence during treatment and for 120 days after the last CJNJ-67652000 (niraparib/abiraterone acetate fixed-dose combination) dose; or

∙ Committed to using an effective method of contraception with their partner during treatment and for 120 days following the last dose of CJNJ-67652000 (niraparib/abiraterone acetate fixed-dose combination)

• Provide written informed consent