Radiation Therapy With or Without Apalutamide in Treating Patients With Recurrent Prostate Cancer, the BALANCE Trial

Inclusion Criteria: * Pathologically (histologically) proven diagnosis of prostate adenocarcinoma; prostatectomy must have been performed within 10 years prior to Step 1 registration and any type of radical prostatectomy is permitted, including retropubic, perineal, laparoscopic or robotically assisted * Post-prostatectomy patients with a detectable serum PSA (\>= 0.1, but =\< 1.0 ng/mL) at study entry (within 90 days of Step 1 registration) and at least one of the following: * Gleason score 7-10 (International Society of Urological Pathology \[ISUP\] grade group 2 to 5) * ISUP grade group: * Grade group 1 = Gleason score =\< 6, * Grade group 2 = Gleason score 3 + 4 = 7, * Grade group 3 = Gleason score 4 + 3 = 7, * Grade group 4 = Gleason score 8, * Grade group 5 = Gleason scores 9 and 10 * \>= T3a disease * Persistent elevation of PSA after prostatectomy measured within 90 days after surgery (PSA never became undetectable) of \> 0.04 but \< 0.2 ng/mL (PSA nadir) * pN0 or pNx * History/physical examination within 90 days prior to Step 1 registration * Karnofsky performance status of 70-100 within 90 days prior to Step 1 registration * Surgical formalin-fixed paraffin-embedded (FFPE) specimen must be available for submission to GenomeDx for genomic analysis on Decipher GRID platform; Note: if Decipher results have already been obtained, in lieu of tissue, results must be submitted to GenomeDx for validation and for GenomeDx to provide the subtypi…