Enzalutamide With or Without Radium Ra 223 Dichloride in Patients With Metastatic, Castration-Resistant Prostate Cancer

Inclusion Criteria: * Men with metastatic, castration resistant prostate cancer involving the bone, which is symptomatic or asymptomatic * Castration resistance will be defined as the development of disease progression, defined as one of the following: * Rising PSA x 2 values \>= 2 weeks apart; minimum absolute PSA value 2 ng/mL * Radiographic progression, with at least 1 new site of metastasis * Symptomatic progression (ex: increase in pain despite stable imaging) AND despite ongoing luteinizing hormone-releasing hormone (LHRH) therapy OR testosterone level \< 50 * Men must have osseous metastases, but the presence of visceral metastases will not exclude patients from participation * Prior external beam radiation therapy (\> 4 weeks prior to enrollment) for palliation of osseous metastatic disease is allowed, provided there is at least one osseous metastasis which has not been irradiated and which can be biopsied * No prior docetaxel or cabazitaxel chemotherapy for metastatic castration-resistant prostate cancer (mCRPC) (men treated with prior docetaxel administered as up-front therapy with androgen deprivation therapy \[ADT\] \> 6 months ago will be eligible); prior abiraterone is allowed * Eastern Cooperative Oncology Group (ECOG) performance status of 0-1 * Hemoglobin \>= 9.5 g/dL * Absolute neutrophil count \>= 1,500 * Platelets \>= 100,000 * Total bilirubin within normal institutional limits * Creatinine clearance (calculated or measured) \> 30 mL/min * At least one risk factor predicting higher likelihood of bone marrow sample yield: elevated alkaline phosphatase, low hemoglobin, or elevated lactate dehydrogenase (LDH) * Ability to understand and the willingness to sign a written informed consent Exclusion Criteria: * Prior treatment with docetaxel or cabazitaxel for mCRPC * Prior treatment with ARN-509 or enzalutamide (there is a grace period for men who wish to enroll and who have recently started enzalutamide for the first time but have taken less than 15 days of therapy) * Concurrent use of androgen deprivation therapy aside from LHRH agonist or antagonist (i.e. bicalutamide, flutamide, nilutamide, abiraterone, ketoconazole, estrogen); there will be a 2 week wash-out period from the last dose of any of these agents until the first dose of enzalutamide on study; patients who have just started enzalutamide for fewer than 5 doses prior to enrollment in the trial are still considered eligible and not subject to wash-out * Concurrent oral corticosteroid use aside from adrenal replacement, or use of other immunosuppressive agents (ex: infliximab); topical or inhaled steroids will be allowed * Received systemic therapy with radionuclides (e.g., strontium-89, samarium- 153, rhenium-186, or rhenium-188, or radium Ra 223 dichloride) for the treatment of bony metastases * History of seizures except for remote with specific etiology which has resolved (ex: alcohol induced seizure); transient ischemic attack (TIA) or cerebrovascular accident (CVA) within last 6 months * Known untreated central nervous system (CNS) metastases; leptomeningeal disease will be an absolute exclusion criterion due to limited life expectancy * Chronic diarrhea \> grade 1, or a diagnosis of Crohn?s or ulcerative colitis * Known hepatitis (hep) B or C, or known cirrhosis (screening for viral hepatitis is not required) * Uncontrolled intercurrent illness such as infection, symptomatic congestive heart failure, unstable angina pectoris, or psychiatric illness which would limit compliance with study requirements * Imminent spinal cord compression based on clinical findings and/or magnetic resonance imaging (MRI); treatment should be completed for spinal cord compression