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 \[CrCl\]); creatinine clearance should be calculated per institutional standard, performed within 28 days of treatment initiation * Serum total bilirubin =\< 1.5 X ULN OR direct bilirubin =\< ULN for subjects with total bilirubin levels \> 1.5 ULN, performed within 28 days of treatment initiation * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 X ULN OR =\< 5 X ULN for subjects with liver metastases, performed within 28 days of treatment initiation * International normalized ratio (INR) or prothrombin time (PT) =\< 1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or partial thromboplastin time (PTT) is within therapeutic range of intended use of anticoagulants (only if submitting to a biopsy), performed within 28 days of treatment initiation * Activated partial thromboplastin time (aPTT) =\< 1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants (only if submitting to a biopsy), performed within 28 days of treatment initiation * Male subjects should agree to use an adequate method of contraception starting with the first dose of study therapy through 120 days after the last dose of study therapy * Have a PSA or radiographic progression on enzalutamide; PSA progression is defined as two consecutive increases in PSA with the second level obtained at least 3 weeks after the first, and the second level of at least 0.5 ng/mL; soft tissue disease progression defined by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 criteria or \>= 2 new lesions on bone scan * Have had either surgical castration OR be on luteinizing hormone-releasing hormone (LHRH) agonist or antagonist therapy with serum testosterone \< 50 ng/dl AND agree to stay on LHRH agonist or antagonist therapy during the study Exclusion Criteria: * Is currently participating in or has participated in a study of an investigational agent or using an investigational device within 4 weeks of the first dose of treatment * Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment; the use of physiologic doses of corticosteroids may be approved after consultation with the sponsor * Has had a prior monoclonal antibody within 4 weeks prior to study day 1 or who has not recovered (i.e., =\< grade 1 or at baseline) from adverse events due to agents administered more than 4 weeks earlier; denosumab is a prohibited medication on study and for 4 weeks prior to day 1 * Has had chemotherapy for castration-resistant disease; chemotherapy for castration-sensitive disease is permitted * Has had prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to study day 1 or who has not recovered (i.e., =\< grade 1 or at baseline) from adverse events due to a previously administered agent * Note: subjects with =\< grade 2 neuropathy are an exception to this criterion and may qualify for the study * Note: if subject received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy * Has a known additional malignancy that is progressing or requires active treatment; exceptions include basal cell carcinoma of the skin, squamous cell carcinoma of the skin, or in situ bladder cancer that has undergone potentially curative therapy * Has known brain metastases and/or carcinomatous meningitis * Has a history of seizure * Has allergy to enzalutamide * Has an active autoimmune disease requiring systemic treatment within the past 3 months or a documented history of clinically severe autoimmune disease, or a syndrome that requires systemic steroids or immunosuppressive agents; a severe autoimmune disease is one that requires a significant medical intervention such as hospitalization; subjects with vitiligo or resolved childhood asthma/atopy would be an exception to this rule; subjects that require intermittent use of bronchodilators or local steroid injections would not be excluded from the study; subjects with hypothyroidism stable on hormone replacement or Sjogren?s syndrome will not be excluded from the study * Has a history of (non-infectious) pneumonitis that required steroids or current pneumonitis * Has an active infection requiring systemic therapy * Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject?s participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator * Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial * Has received prior therapy with an anti-programmed cell death (PD)-1, anti-PD-ligand (L)1, anti-PD-L2, anti-cluster of differentiation (CD)137, or anti-cytotoxic T-lymphocyte-associated antigen-4 (CTLA-4) antibody (including ipilimumab or any other antibody or drug specifically targeting T-cell co-stimulation or checkpoint pathways); previous treatment with sipuleucel-T is permitted * Has plans to receive cytotoxic chemotherapy, immune checkpoint inhibitors (eg CTLA-4 blockade), sipuleucel-T, radiopharmaceuticals, abiraterone or other experimental therapy during this study period * Has a known history of human immunodeficiency virus (HIV) (HIV 1/2 antibodies) * Has known active hepatitis B (e.g., hepatitis B virus surface antigen \[HBsAg\] reactive) or hepatitis C (e.g., hepatitis C virus \[HCV\] ribonucleic acid \[RNA\] \[qualitative\] is detected) * Has received a live vaccine within 30 days prior to the first dose of trial treatment * Has rapid progression of visceral disease and, thus is a candidate for docetaxel; this determination will be at the discretion of the treating physician