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…