A Study of Salvage Radiotherapy With or Without Enzalutamide in Recurrent Prostate Cancer Following Surgery

Inclusion Criteria: * Pathologically (histologically) proven adenocarcinoma confirmed by prostatectomy performed within 10 years prior to registration and any type of radical prostatectomy is permitted, including retropubic, perineal, laparoscopic or robotically assisted. * Prostate-specific antigen (PSA) level (≥ 0.2 ng/mL) within 120 days prior to registration. Patients must have a PSA ≥ 0.2 ng/mL prior to starting ADT. For patients being followed by an ultrasensitive PSA assay, a serum PSA concentration of ≥ 0.10 ng/mL will be considered eligible. * GnRH analog may be started no more than 42 days prior study entry. * Hemoglobin ≥ 9.0 g/dL, independent of transfusion and/or growth factors within 90 days prior to registration. * Platelet count ≥ 75,000 x 10\^9/µL independent of transfusion and/or growth factors within 90 days prior to registration. * At least 1 of the following aggressive features: * Gleason score of 8-10 (note any Gleason score is eligible) * Seminal vesicle invasion (SVI) (note any pT stage American Joint Committee on Cancer (AJCC) v8.0 is eligible but a pT stage ≥ pT3b is considered aggressive) * Locoregional node involvement at radical prostatectomy (RP) (pN1) * Persistently elevated PSA post-RP nadir (PEPP) defined as PSA \> 0.1 ng/mL after radical prostatectomy * PSA ≥ 0.7 ng/mL * Serum albumin ≥ 3.0 g/dL within 90 days prior to registration * Glomerular filtration rate (GFR) ≥35 mL/min estimated by Cockcroft-Gault or measured directly by 24 hour urine creatinine within 90 days prior to registration. * Serum total bilirubin ≤1.5 × upper limit of normal (ULN) (Note: In subjects with Gilbert's syndrome, if total bilirubin is \>1.5 × ULN, measure direct and indirect bilirubin and if direct bilirubin is ≤1.5 × ULN, subject is eligible) within 90 days prior to registration. * Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) \<2.5 × ULN within 90 days prior to registration. * History and physical with Eastern Cooperative Oncology Group (ECOG) Performance Status 0-1 or within 90 days prior to registration. Exclusion Criteria: * Definitive clinical or radiologic evidence of metastatic disease with the exception of locoregional lymph nodes. * Prior invasive malignancy (except non-melanomatous skin cancer carcinoma in situ of the male breast, penis, oral cavity, or stage Ta of the bladder, or stage I completely resected melanoma) unless disease free for a minimum of 2 years). * Prior systemic chemotherapy for the study cancer. Note: prior chemotherapy for a different cancer is allowable. * Prior radiotherapy to the region of the study cancer that would result in overlap of radiation therapy fields. * History of any of the following: * Documented inflammatory bowel disease * Transmural myocardial infarction within the last 4 months prior to registration. * New York Heart Association Functional Classification III/IV within 4 months prior to registration. * Unstable angina and/or congestive heart failure requiring hospitalization within the last 4 months prior to registration * History of loss of consciousness or transient ischemic attack within 12 months prior to randomization * History of seizure disorder or condition that may predispose to seizure (e.g. prior cortical stroke or significant brain trauma) * History of uncontrolled hypertension defined as a sustained systolic blood pressure in excess of 150 mmHg or a sustained diastolic blood pressure in excess of 90 mmHg despite optimized antihypertensive therapy. * History of repeated falls and fractures over the past 12 months that in the opinion of the treating investigator would put the patient at risk for poor bone outcomes from androgen receptor targeted therapy * Known gastrointestinal disorder affecting absorption of oral medications. * Active uncontrolled infection defined as an identified infectious condition that requires active therapy that has not yet been completed. * HIV positive patients with CD4 count \< 200 cells/microliter within 30 days prior to registration OR HIV patients under treatment with highly active antiretroviral therapy (HAART) within 30 days prior to registration regardless of CD4 count. Note: HIV testing is not required for eligibility for this protocol as it is self-reported. This exclusion criterion is necessary because the treatments involved in this protocol may be immunosuppressive and/or interact with HAART.