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This phase II trial tests whether relugolix and radiation therapy works to shrink tumors in patients with prostate cancer that has spread in a limited way to 1 to 5 other parts of the body (oligometastatic). Testosterone can cause the growth of prostate cancer cells. Relugolix lowers the amount of testosterone made by the body. This may help stop the growth of tumor cells that need testosterone to grow. Giving relugolix with radiation therapy may help lower the chance of prostate cancer growing or spreading.

PRIMARY OBJECTIVE: I. Compare conventional radiological progression-free survival (rPFS) for positron emission tomography (PET)-detected, biochemically recurrent, oligometastatic, castration-sensitive prostate cancer patients treated with stereotactic ablative body radiation therapy (SABR) plus placebo versus (vs.) SABR plus relugolix. SECONDARY OBJECTIVES: I. Compare conventional or PET-based radiological progression-free survival (prPFS) between treatment arms. II. Compare patient-reported sexual and hormonal quality of life as assessed by corresponding Expanded Prostate Cancer Index Composite Short Form (EPIC-26) domains between treatment arms. III. Compare other measures of quality of life obtained from the European Quality of Life Five Dimension Five Level Scale Questionnaire (EQ5D-5L), European Organization for Research and Treatment of Cancer (EORTC) Quality of Life Questionnaire Core 30 (QLQ-30), and Patient Reported Outcomes Measurement Information System (PROMIS) Fatigue instruments between the two treatment arms. IV. Compare time to salvage therapy and time to castration-resistance between treatment arms. V. Compare local progression (SABR-targeted lesion), biochemical progression, distant metastases, prostate cancer-specific mortality, metastasis-free survival, and overall survival between treatment arms. VI. Determine adverse events rates and compare rates between the two treatment arms.