• 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