Radium Ra 223 Dichloride, Hormone Therapy and Stereotactic Body Radiation Therapy in Treating Patients With Metastatic Prostate Cancer

Inclusion Criteria: * Documented informed consent of participant and/or legally authorized representative * Agreement to provide archival primary or metastatic tumor tissue if available * Eastern Cooperative Oncology Group (ECOG) =\< 2 * Life expectancy \> 12 months * Histologic diagnosis of prostate adenocarcinoma \* Pure small cell carcinoma will be excluded; however, component of neuroendocrine /small cell differentiation will be allowed provided that adenocarcinoma constitutes majority of the tissue specimen * Stage M1 \* Metastatic disease can be documented by bone scan or computed tomography (CT) scan or magnetic resonance imaging (MRI) or positron emission tomography (PET)/CT or the combination of these tests * Up to 4 metastatic lesions: * Must have at least 1 bone lesion AND each non-visceral lesion should be less than 5 cm * Visceral lesions will be limited to one lung lesion (\< 2 cm) or one lymph node; no liver lesions allowed; lymph nodes allowed provided they are not in a field of prior radiation, and if amenable to SBRT (to be reviewed by principal investigator \[PI\]) * Two lesions can be in close proximity (i.e. within 5 cm of each other) if they meet radiation SBRT normal tissue toxicity requirements * If have untreated primary prostate cancer: must undergo debulking prostatectomy * If had prior definitive radiation therapy to the prostate: no evidence of locally persistent or recurrent prostate cancer on digital rectal exam (DRE) and imaging studies (CT or MRI); retreatment to local residual-recurrent disease will result in potential eligibility to be reviewed by PI on a case-by-case basis * Does not have castration resistant disease \* Castration resistance defined as progression of disease despite serum testosterone level of \< 50 ng/dL * PSA \>= 0.2 prior to start of androgen deprivation treatment * Initiated 28 (+ 7) days of androgen deprivation therapy (ADT) prior to day 1 of protocol therapy \* Only luteinizing hormone-releasing hormone (LHRH) agonist/antagonist treatment is considered ADT, bicalutamide or other antiandrogens used alone do not count * May have received prior hormonal therapy in the context of definitive treatment of a primary tumor \* Patients may have had one prior systemic non-chemotherapeutic treatment (i.e. immunotherapy, receptor tyrosine kinase inhibitor, antiangiogenic agent, differentiating agent) for recurrent or metastatic disease * Must have refused standard of care chemotherapy for metastatic disease * Recovered from all acute side-effects (except alopecia) related to previous systemic therapy * Absolute neutrophil count (ANC) \>= 1,500/mm\^3 (to be performed within 14 days prior to day 1 of protocol therapy) \* NOTE: growth factor support is not permitted to normalize baseline ANC parameters, however subsequent growth factor administration is permitted as standard supportive care * Platelets \>= 100,000/mm\^3 (to be performed within 14 days prior to day 1 of protocol therapy) \* NOTE: transfusion of blood products are not allowed to normalize baseline blood parameters, however subsequent transfusions are allowed per standard supportive care guidelines * Hemoglobin (HgB) \>= 9.0 g/dL (to be performed within 14 days prior to day 1 of protocol therapy) \* NOTE: transfusion of blood products are not allowed to normalize baseline blood parameters, however subsequent transfusions are allowed per standard supportive care guidelines * Total serum bilirubin =\< 2 x upper limit of normal (ULN) (to be performed within 14 days prior to day 1 of protocol therapy) * Aspartate aminotransferase (AST) =\< 2.5 x ULN (to be performed within 14 days prior to day 1 of protocol therapy) * Alanine aminotransferase (ALT) =\< 2.5 x ULN (to be performed within 14 days prior to day 1 of protocol therapy) * Creatinine =\< 2.5 mg/dL (to be performed within 14 days prior to day 1 of protocol therapy) Exclusion Criteria: * Prior radium Ra 223 dichloride * Prior or concomitant chemotherapy for metastatic or recurrent disease with the following exceptions: * Prior chemotherapy for local primary disease is permitted * Bisphosphonates or receptor activator of nuclear factor kappa-Β (RANK) ligand inhibitors are allowed at doses and schedule consistent with the treatment or prevention of osteoporosis * Prior radiation treatment for metastatic disease * Concomitant radiation treatment to primary prostate site * Orchiectomy * Unstable medical comorbidities (i.e. uncontrolled cardiac comorbidities) * Metastases that in the judgment of investigator-radiologist are not amenable to SBRT * History of brain metastases or who currently have treated or untreated brain metastases * Uncontrolled human immunodeficiency virus (HIV) infection * Any other condition that would, in the investigator's judgement, contraindicate the patient's participation in the clinical study due to safety concerns with clinical study procedures * Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)