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

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

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)

* 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

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)

What this study is about