Enzalutamide and Indomethacin in Treating Patients With Recurrent or Metastatic Hormone-Resistant Prostate Cancer

Inclusion Criteria: * Patients must have histologically or cytologically confirmed prostate cancer (CaP); CaP can be recurrent disease after definitive therapy (radical prostatectomy or radiation therapy) for localized CaP, or metastatic CaP * Patients must have CaP deemed to be castration-resistant by one or more of the following criteria (despite androgen deprivation when applicable): * Progression of unidimensionally measurable disease assessed within 42 days prior to initial administration of drug * Progression of evaluable but not measurable disease assessed within 42 days prior to initial administration of drug for PSA evaluation and for imaging studies (e.g, bone scans) * Rising PSA, defined as at least two consecutive rises in PSA to be documented over a reference value (measure 1); the first rising PSA (measure 2) should be taken at least 7 days after the reference value; a third confirmatory PSA measure (2nd beyond the reference level) should be greater than the second measure, and it must be obtained at least 7 days after the 2nd measure; if this is not the case, a fourth PSA measurement is required to be taken and be greater than the second measure * Measurable disease is not required * Patients who have measurable disease must have had X-rays, scans or physical examinations used for tumor measurement completed within 28 days prior to initial administration of drug * Patients must have non-measurable disease (such as nuclear medicine bone scans) and non-target lesions (such as PSA level) assessed within 28 days prior to initial administration of drug * Soft tissue disease that has been radiated within two months prior to registration is not assessable as measurable disease; soft tissue disease that has been radiated two or more months prior to registration is assessable as measurable disease provided that the lesion has progressed following radiation; as the biology of previously irradiated tumors may be different from non-irradiated tumors, patients must have at least one measurable lesion outside the previously irradiated region in order to be considered to have measurable disease * If PSA is the only indicator of disease and patients do not have any metastatic disease, PSA value must be 5.0 or higher * Patients must have been surgically or medically castrated; if the method of castration was luteinizing hormone-releasing hormone (LHRH) agonists (leuprolide or goserelin) or antagonists (degarelix), then the patient must be willing to continue the use of LHRH agonists or antagonists; serum testosterone must be at castration levels (\< 50 ng/dL) within 3 months prior to registration * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Life expectancy of greater than 6 months * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Total bilirubin within normal institutional limits * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) =\< 1.5 x institutional upper limit of normal * Creatinine =\< 1.5 x institutional upper limit of normal * Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of enzalutamide administration * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy within 4 weeks prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier * Patients who are receiving any other investigational agents within the preceding 4 weeks * Patients on herbs or other alternative medicines for the treatment of prostate cancer, including but not limited to saw palmetto, PC-SPES * Patient has received enzalutamide or ketoconazole for the treatment of prostate cancer; however, previous treatment with other hormonal therapy (bicalutamide, abiraterone, flutamide, and nilutamide) or chemotherapy (docetaxel, cabazitaxel, or mitoxantrone) is allowed * Other malignancies within the past 3 years except for adequately treated basal or squamous cell carcinomas of the skin or other stage 0 or I cancers * Patients with known brain metastases should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events * History of allergic reactions attributed to compounds of similar chemical or biologic composition to enzalutamide or indomethacin * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible * Impairment of gastrointestinal function or gastrointestinal disease that may significantly alter the absorption of drugs (e.g., ulcerative disease, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome, or small bowel resection) * Patients with an active bleeding diathesis * History of noncompliance to medical regimens * Patients unwilling to or unable to comply with the protocol * Patients with symptomatic metastatic prostate cancer such as moderate to severe pain, impaired organ function, or spinal cord compression will be excluded from this study unless these issues have been taken care of * Patients with a history of seizure disorder, underlying brain injury with loss of consciousness, transient ischemic attack within the past 12 months, cerebral vascular accident, brain metastases, brain arteriovenous malformation * Patients with a history of peptic ulcer disease or gastrointestinal bleeding