CJNJ-67652000 and Prednisone for Treatment of Metastatic Castration-Resistant Prostate Cancer and SPOP Gene Mutations

Inclusion Criteria:

* 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

Exclusion Criteria:

* Prior treatment with PARP inhibitor or platinum chemotherapy
* Historical or current diagnosis of myelodysplastic syndrome or myeloid malignancy
* Any of the following prior therapies:

  * Surgery =\< 3 weeks prior to registration
  * Chemotherapy =\< 2 weeks prior to registration
* Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens
* Clinician assessed prognosis of less than 16 weeks
* Human immunodeficiency virus (HIV) positive subjects with 1 or more of the following:

  * Not receiving highly active antiretroviral therapy
  * Receiving antiretroviral therapy that may interfere with the study drug (consult the sponsor for review of medication prior to enrollment)
  * A change in antiretroviral therapy within 6 months of the start of screening (except if, after consultation with the sponsor-investigator on exclusion criterion, a change is made to avoid a potential drug-drug interaction with the study drug)
  * CD4 count \< 350 at screening
  * An acquired immunodeficiency syndrome-defining opportunistic infection within 6 months of the start of screening
* Uncontrolled intercurrent illness including, but not limited to:

  * Ongoing or active infection
  * Symptomatic congestive heart failure (left ventricular ejection fraction \[LVEF\] \< 50% or New York Heart Association \[NYHA\] class III or IV heart failure)
  * Unstable angina pectoris
  * Cardiac arrhythmia
  * Myocardial infarction within the last 6 months
  * Uncontrolled hypertension (systolic blood pressure \>= 160 mmHg or diastolic blood pressure \[BP\] \>= 95 mmHg). Subjects with a history of hypertension are allowed provided blood pressure is controlled by anti-hypertensive treatment
  * Or psychiatric illness/social situations that would limit compliance with study requirements
* Receiving any other investigational agent which would be considered as a treatment for the primary neoplasm
* Other active malignancy =\< 3 years prior to registration

  * EXCEPTIONS: Non-melanotic skin cancer, carcinoma-in-situ of the cervix, or malignancy not expected to require therapy (systemic or radiation) in the next 1 year
* History of myocardial infarction =\< 6 months
* Symptomatic brain metastases
* Current evidence of any of the following:

  * Any medical condition that would make prednisone use contraindicated
  * Any chronic medical condition requiring a higher dose of corticosteroid than 10 mg prednisone (or equivalent once daily