Pembrolizumab in Treating Patients With Metastatic Castration Resistant Prostate Cancer Previously Treated With Enzalutamide

Inclusion Criteria: * ENTRY CRITERIA: Metastatic, castration resistant prostate cancer progressing on enzalutamide after initial response to enzalutamide * Histologically or cytologically confirmed adenocarcinoma of the prostate without pure small cell carcinoma; patients without histologically confirmed adenocarcinoma may be eligible if both the treating physician and the study principal investigator (PI) agree that the patient?s history is unambiguously indicative of advanced adenocarcinoma * Be willing and able to provide written informed consent/assent for the trial * Be \>= 18 years of age on day of signing informed consent * Have metastatic disease * Have permission to access tissue from an archival tissue sample; (absence of archival tissue will not preclude trial participation) * Has a metastatic deposit that can be biopsied * Have a performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG) performance scale * Absolute neutrophil count (ANC) \>= 1,500/mcL, performed within 28 days of treatment initiation * Platelets \>= 100,000/mcL, performed within 28 days of treatment initiation * Hemoglobin \>= 9 g/dL or \>= 5.6 mmol/L, performed within 28 days of treatment initiation * Serum creatinine =\< 1.5 X upper limit of normal (ULN) OR measured or calculated creatinine clearance \>= 60 mL/min for subject with creatinine levels \> 1.5 X institutional ULN (glomerular filtration rate \[GFR\] can also be used in place of creatinine or creatinine clearance \…