Antiandrogen Therapy and Radiation Therapy With or Without Docetaxel in Treating Patients With Prostate Cancer That Has Been Removed by Surgery

Inclusion Criteria: * Patients post-prostatectomy with baseline Gleason \>= 7 (per prostatectomy pathology) * Baseline PSA prior to start of androgen deprivation therapy nadir \>= 0.2 ng/ml (post-operative value is never undetectable) obtained prior to step 1 registration * Baseline testosterone level obtained post-prostatectomy prior to start of androgen deprivation therapy and prior to step 1 registration * Pathologically (histologically) proven diagnosis of adenocarcinoma of the prostate as confirmed at time of prostatectomy; prostatectomy must have been performed within 365 days (1 year) prior to step 1 registrationand any type of radical prostatectomy is permitted, including retropubic, perineal, laparoscopic or robotically assisted; (please note: Prior ablative treatment for benign prostatic hypertrophy or focal high-intensity focused ultrasound therapy \[HIFU\] prior to prostatectomy is allowed) * Surgical formalin-fixed paraffin-embedded (FFPE) specimen must be available for submission to GenomeDx for genomic analysis on DECIPHER GRID platform * Please note: If a patient already has a Decipher risk score and meets all of the other eligibility criteria, the patient is eligible to be registered; however, the Decipher risk report will need to be submitted to GenomeDx for validation * Prior androgen deprivation (luteinizing hormone-releasing hormone \[LHRH\] agonist and/or non-steroidal anti-androgen) is allowed if: * Androgen deprivation therapy was initiated within 30 days prior to study enrollment * Androgen deprivation therapy was given for ≤ 90 days duration prior to radical prostatectomy * Please note: Finasteride or dutasteride must be stopped before treatment but should not determine eligibility * Pathologically lymph node negative by pelvic lymphadenectomy (pN0) or lymph node status pathologically unknown (undissected pelvic lymph nodes \[pNx\]) * Any pT-stage based on American Joint Committee on Cancer 7th edition eligible; study entry will be based on the following diagnostic workup: * History/physical examination within 60 days prior to step 1 registration * Negative distant metastatic workup: * A computed tomography (CT) scan of the abdomen and pelvis (with contrast \[CT without contrast is permitted if the patient is not a candidate for contrast, i.e., renal function or allergy\]) or magnetic resonance imaging (MRI) of the pelvis within 120 days prior to step 1 registration; (Please note: Lymph nodes will be considered negative (NO)if they are =\< 1.5 cm short axis); * Bone scan within 120 days prior to step 1 registration; (please note: a sodium fluoride \[NaF\] positron emission tomography \[PET\]/CT is an acceptable substitute and if the bone scan is suspicious, a plain x-ray, CT scan, NaF PET/CT and/or MRI must be obtained to rule out metastasis; Axumin scans are not allowed for determination of eligibility \[e.g. a positive Axumin can in the setting of negative bonescan and CT does not exclude a patient from being eligible for enrollment\]). * Eastern Cooperative Oncology Group (ECOG) performance status of =\< 1 within 60 days prior to step 1 registration * Platelets \>= 100,000 cell/mm\^3 (within 60 days prior to step 1 registration based upon a complete blood count \[CBC\]) * Hemoglobin \>= 10.0 g/dl (Note: The use of transfusion or other intervention to achieve hemoglobin \[Hgb\] \>= 10.0 g/dl is NOT allowed) (within 60 days prior to step 1 registration based upon a CBC) * Absolute neutrophil count \>= 1500 cells/mm\^3 (within 60 days prior to step 1 registration based upon a CBC) * Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) \< 1.5 x the upper limit of normal (within 60 days prior to step 1 registration) * Total bilirubin (=\< 1.5 mg/dl) normal unless history of Gilbert's syndrome (within 60 days prior to step 1 registration) * The patient or a legally authorized representative must provide study-specific informed consent prior to step 1 registration Exclusion Criteria: * Definitive clinical or radiologic evidence of metastatic disease * Prior invasive malignancy (except non-melanomatous skin cancer or other in-situ malignancies, or stage Ta bladder cancer) unless disease free for a minimum of 2 years * Prior radiotherapy to the region of the study cancer that would result in overlap of radiation therapy fields * Prior systemic chemotherapy for the study cancer; note that prior chemotherapy for a different cancer is allowable if completed more than two years prior to step 1 registration; prior androgen deprivation is allowed * Prior whole gland ablative therapy (i.e. cryoablation or high intensity focused ultrasound \[HIFU\]) for prostate cancer is not allowed * Prostatectomy performed greater than 365 days (1 year) prior to step 1 registration * Severe and/or active co-morbidity defined as follows: * History of inflammatory bowel disease * History of active hepatitis B or C; blood tests are not required to determine if the patient has had hepatitis B or C, unless the patient reports a history of hepatitis * Unstable angina and/or congestive heart failure requiring hospitalization within the last 6 months * Transmural myocardial infarction within the last 6 months * Acute bacterial or fungal infection requiring intravenous antibiotics at the time of step 1 registration * Chronic obstructive pulmonary disease exacerbation or other respiratory illness requiring hospitalization within 15 days of step 1 registration or precluding study therapy at the time of step 1 registration * Uncontrolled severe illness or medical condition (including uncontrolled diabetes), which in the judgment of the treating physician would make the administration of chemotherapy inadvisable * Human immunodeficiency virus (HIV) positive with cluster of differentiation 4 (CD4) count \< 200 cells/microliter; note that patients who are HIV positive are eligible, provided they are under treatment with highly active antiretroviral therapy (HAART) and have a CD4 count \>= 200 cells/microliter within 30 days prior to step 1 registration; note also that HIV testing is not required for eligibility for this protocol