Testing the Addition of a New Anti-Cancer Drug, Niraparib, to the Usual Treatment (Hormone and Radiation Therapy) for Prostate Cancer With a High Chance of Recurring

Inclusion Criteria:

* Histologically confirmed (within 180 days prior to registration) adenocarcinoma of the prostate at high risk for recurrence as determined by the following criteria, according to American Joint Committee on Cancer (AJCC) 8th edition:

  * Phase I enrollment

    * Gleason \>= 9, PSA =\< 150 ng/mL, any T-stage
  * Phase II enrollment

    * Gleason \>= 9, PSA =\< 150 ng/mL, any T-stage
    * Gleason 8, PSA \< 20 ng/mL, and \>= T2
    * Gleason 8, PSA \>= 20-150 ng/mL, any T-stage
    * Gleason 7, PSA \>= 20-150 ng/mL, any T-stage
* No distant metastases as evaluated by:

  * Bone scan 90 days prior to registration
  * Lymph node assessment by computed tomography (CT) or magnetic resonance (MR) of pelvis or nodal sampling within 90 days prior to registration (Please note: Lymph nodes will be considered negative \[N0\] if they are \< 1.5 cm short axis)
* History/physical examination within 90 days prior to registration
* Age \>= 18
* Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 within 180 days prior to registration
* Pretreatment serum PSA, obtained prior to any androgen suppression therapy and within 180 days of registration
* Phase I patients: Prior androgen suppression for prostate cancer is not allowed prior to registration
* Phase II patients: Prior androgen suppression for prostate cancer is allowed =\< 45 days prior to registration
* Hemoglobin \>= 9.0 g/dL (within 90 days prior to registration)
* Platelets \>= 100,000 cells/mm\^3 (within 90 days prior to registration)
* Absolute neutrophil count (ANC) \>= 1.5 x 10\^9/L (within 90 days prior to registration)
* Serum creatinine =\<1.5 x upper limit of normal (ULN) OR a calculated creatinine clearance \>= 30 mL/min estimated using Cockcroft-Gault equation (within 90 days prior to registration)
* Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 3.0 x ULN (within 90 days prior to registration)
* Serum albumin \>= 3 g/dL (within 90 days prior to registration)
* Serum potassium \>= 3.5 mmol/L (within 90 days prior to registration)
* Serum total bilirubin =\< 1.5 x ULN or direct bilirubin =\< 1 x ULN (Note: in subjects with Gilberts 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) (within 90 days prior to registration)
* Men of child-producing potential must be willing to consent to use effective contraception while on treatment and for at least 3 months afterwards
* The patient or a legally authorized representative must provide study-specific informed consent prior to study entry

Exclusion Criteria:

* PSA \> 150 ng/mL
* Definitive clinical or radiologic evidence of metastatic disease
* Pathologically positive lymph nodes or nodes \> 1.5 cm short axis on CT or MR imaging
* Prior radical prostatectomy, cryosurgery for prostate cancer, or bilateral orchiectomy for any reason
* Any active malignancy within 2 years of study registration that may alter the course of prostate cancer treatment
* Prior systemic therapy for prostate cancer; note that prior therapy for a different cancer is allowable
* Prior radiotherapy, including brachytherapy, to the region of the prostate that would result in overlap of radiation therapy fields
* Current treatment with first generation anti-androgens (bicalutamide, nilutamide, flutamide). For patients enrolled to phase II, if prior anti-androgens were administered, a washout period of \>= 30 days is required prior to enrollment
* Severe, active co-morbidity, defined as follows:

  * Unstable angina and/or congestive heart failure requiring hospitalization within the last 6 months
  * Transmural myocardial infarction within the last 6 months
  * Acute bacterial or fungal infection requiring intravenous antibiotics at the time of registration
  * Uncontrolled acquired immune deficiency syndrome (AIDS) based upon current Centers for Disease Control and Prevention (CDC) definition
  * Presence of uncontrolled hypertension (persistent systolic blood pressure \[BP\] \>=160 mmHg or diastolic BP \>= 100 mmHg). Subjects with a history of hypertension are allowed, provided that BP is controlled to within these limits by anti-hypertensive treatment
* Prior allergic reaction to the drugs involved in this protocol (including known allergies, hypersensitivity or intolerance to the excipients of niraparib)
* Human immunodeficiency virus (HIV) positive with CD4 count \< 200 cells/microliter

  * Note that patients who are HIV positive are eligible, provided they have a CD4 count \>= 200 cells/microliter within 90 days prior to registration. Patients receiving treatment with highly active antiretroviral therapy (HAART) will not be eligible due to concern for radiosensitization
  * Note also that HIV testing is not required for eligibility for this protocol. This exclusion criterion is necessary because the treatments involved in this protocol may be affected by these drugs
* Any history or current diagnosis of myelodysplastic syndrome (MDS)/acute myeloid leukemia (AML)
* Prior or current treatment with PARP inhibitor