Testing the Addition of the Drug Relugolix to the Usual Radiation Therapy for Advanced-Stage Prostate Cancer, The NRG Promethean Study

Inclusion Criteria:

* Pathologically (histologically or cytologically) proven diagnosis of prostate adenocarcinoma at any anatomical location (for example, prostate, metastatic site), including intraductal or ductal carcinoma, at any time before registration
* Age \>= 18 years
* Eastern Cooperative Oncology Group (ECOG) performance status 0-2 within 180 days prior to registration
* Prior curative-intent treatment to the prostate, by either:

  * External beam and/or brachytherapy to: Prostate alone, prostate and seminal vesicles, prostate and pelvic nodes, or radiation to all three sites
  * Radical prostatectomy alone, radical prostatectomy plus postoperative radiotherapy to the prostate bed, or radical prostatectomy plus postoperative radiotherapy to the pelvic nodes.

    * Note: Patients who have received curative intent with radiation prior to prostatectomy are eligible and should be categorized as RT to Intact Prostate since that was the first curative intent
* Must meet study entry criteria based on the following diagnostic workup within 120 days prior to registration:

  * History and physical examination;
  * Fluciclovine or PSMA PET scan;
  * PET must be combined with either CT or MRI, but a diagnostic CT or MRI reading/interpretation is not required
* 1 - 5 oligometastatic lesions in bone and/or nodal/soft tissue (non-abutting nodes are counted separately) sites on fluciclovine or PSMA PET within 180 days prior to registration and includes at least ONE of the following:

  * Bone - each metastasis is counted (for example, 2 distinct lesions in the right ilium count as 2 oligometastatic lesions)
  * Extrapelvic Nodal/ soft tissue - requires at least one extrapelvic inguinal or a nodal/soft tissue lesion superior to the iliac bifurcation (that is, American Joint Committee on Cancer \[AJCC\] M1a version 8)
  * Note: Although a patient must have bone and/or extrapelvic disease to be eligible, when counting the number of oligometastatic lesions, each lymph node lesion, whether pelvic or extrapelvic, is counted (for example, 2 distinct lymph nodes in the right external iliac basin count as 2 oligometastatic lesions; one extrapelvic and one pelvic node count as 2 oligometastic lesions, etc)
* Serum total prostate-specific antigen (PSA) =\< 10.0 ng/mL that also meets ONE of the following PSA recurrence definitions:

  * If patient has received-radiation therapy to intact prostate, either

    * PSA \> post-RT nadir PSA + 2 ng/mL obtained within 180 days prior to registration, or
    * PSA \> 0.2 ng/mL with at least two rises from post-treatment nadir with the most recent PSA within 180 days prior to registration
  * If patient has received a radical prostatectomy with or without post-op RT, either

    * Current PSA \> 0.2 ng/mL, with a second confirmatory PSA \> 0.2 ng/mL, with most recent PSA obtained within 180 days prior to registration, or
    * Two consecutive PSA rises from post-operative nadir, with most recent PSA obtained within 180 days prior to registration
* Must have \>= 3 PSA values within the last two years since end of primary treatment or within the last 2 years prior to registration, whichever is less

  * Note: PSA doubling time must be calculated by entering all PSA values since end of primary treatment or within the last 2 years prior to registration (whichever is less) into the PSA Doubling Time Calculator found at MDCalc.com
* Serum total testosterone \>= 100 ng/dL within 180 days prior to registration

  * Note: Prior androgen deprivation therapy (other than bilateral orchiectomy) is allowed if discontinued prior to registration and serum total testosterone is \>= 100 ng/dL
* Total bilirubin: =\< 1.5 x institutional upper limit of normal (ULN) (Note: In subjects with Gilbert's syndrome, if total bilirubin is \> 1.5 x ULN, subject is eligible if direct bilirubin is =\< 1.5 x ULN) (within 180 days prior to registration)
* Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]): =\< 2.5 x institutional ULN (within 180 days prior to registration)
* For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated

  * Note: Known positive test for hepatitis B virus surface antigen (HBV sAg) indicating acute or chronic infection would make the patient ineligible unless the viral load becomes undetectable on suppressive therapy. Patients who are immune to hepatitis B (anti-hepatitis B surface antibody positive) are eligible (e.g. patients immunized against hepatitis B)
* Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load

  * Note: Known positive test for hepatitis C virus ribonucleic acid (HCV RNA) indicating acute or chronic infection would make the patient ineligible unless the viral load becomes undetectable on suppressive therapy
* Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial
* The patient must agree to use a highly effective contraception (even men with vasectomies) if he is having sex with a woman of childbearing potential or with a woman who is pregnant while on study drug and for 2 weeks following the last dose of study drug
* The patient or a legally authorized representative must provide study-specific informed consent prior to study entry and, for patients treated in the United States (U.S.), authorization permitting release of personal health information

Exclusion Criteria:

* Currently on androgen deprivation or anti-androgen therapy
* Spinal cord compression, or spinal intramedullary, brain, and/or visceral (for example liver, etc.) metastasis

  * Note: Spinal metastases (PET-detected) with epidural extension are eligible if there is \> 0.3 cm spatial separation between the gross tumor volume and spinal cord. Lung metastases are eligible
* Biopsy-proven prostatic carcinoma with signet-ring, sarcomatoid, or neuroendocrine features (for example, small cell)
* Prior metastatic or non-metastatic, invasive malignancy (except non metastatic, non-melanomatous skin cancer) unless continuously disease free for \>= 3 years
* Prior chemotherapy for prostate cancer or bilateral orchiectomy

  * Note: Prior chemotherapy for a different cancer is allowed if continuously disease-free for \>= 3 years
* Prior high dose radiotherapy to a lesion (i.e. oligometastatic recurrence by PET)

  * Note: Lesions included in or near a previously irradiated planning target volume (PTV) are eligible as long as previous delivered dose is estimated to be less than an EQD2 of 50 Gy
* Inability to treat all oligometastatic sites with radiotherapy in the judgement of the investigator
* Intrapelvic lymph nodes as only site of prostate cancer recurrence
* Inability to swallow whole, undivided, unchewed, and uncrushed pills
* Known gastrointestinal disorder affecting oral medication absorption
* Co-morbidity defined as follows:

  * Patients with any comorbidities that would prohibit completion of protocol specified therapy
  * Inflammatory bowel disease in patients in whom abdominopelvic radiotherapy is planned
  * History of congenital long QT syndrome
  * Current severe or unstable angina
  * New York Heart Association functional classification III/IV heart failure (Note: Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association functional classification)