This phase II trial studies how well radiation therapy with or without apalutamide works in treating patients with prostate cancer that has come back (recurrent). Radiation therapy uses high energy x-ray to kill tumor cells and shrink tumors. Androgen can cause the growth of prostate cancer cells. Drugs, such as apalutamide, may lessen the amount of androgen made by the body. Giving radiation therapy and apalutamide may work better at treating prostate cancer compared to radiation therapy alone.

PRIMARY OBJECTIVE: I. To determine whether, in men with post-prostatectomy prostate-specific antigen (PSA) recurrences, salvage radiation (SRT) with enhanced anti-androgen therapy with apalutamide will improve biochemical progression-free survival (bPFS) compared to SRT alone. SECONDARY OBJECTIVES: I. To assess whether molecular stratification by the PAM50 gene expression clustering will identify subsets of prostate cancer (luminal A or basal, luminal B) which derive the greatest benefit from anti-androgen therapy. II. To assess overall survival. III. To assess cancer-specific mortality. IV. To assess metastasis-free survival. V. To assess distant metastasis. VI. To assess local-regional progression. VII. To assess PSA nadir during first year of treatment and prior to initiation of any hormonal salvage therapy. VIII. To assess initiation of salvage hormonal therapy. IX. To assess PSA with a non-castrate testosterone at 1 and 3 years post randomization: PSA \< 0.1 ng/ml and testosterone \>= 50 ng/dl. X. To assess acute and late physician-reported morbidity (per the Common Terminology Criteria for Adverse Events \[CTCAE\] version 5.0) after SRT +/- apalutamide. XI. To assess acute and late patient-reported symptomatic adverse events morbidity (per the patient reported outcomes \[PRO\]-CTCAE) after SRT +/- apalutamide. XII. To assess testosterone levels at 3, 6, 9, 12, and 36 months post randomization. EXPLORATORY OBJECTIVE: I. To assess the prognostic and predictive value of the genomic classifier Decipher. OUTLINE: Patients are randomized to 1 of 2 arms. ARM 1: Patients undergo external beam radiation therapy on day 1 for 7-8 weeks. Beginning on day of radiation therapy, patients receive placebo orally (PO) once daily (QD) on days 1-30. Treatment repeats every 30 days for up to 6 cycles in the absence of disease progression or unacceptable toxicity. ARM 2: Patients undergo external beam radiation therapy on day 1 for 7-8 weeks. Beginning on day of radiation therapy, patients receive apalutamide PO QD on days 1-30. Treatment repeats every 30 days for up to 6 cycles in the absence of disease progression or unacceptable toxicity. After completion of study treatment, patients are followed up every 3 months for 2 years, then every 6 months for 3 years, and then yearly thereafter.