Pembrolizumab and Cryosurgery in Treating Patients With Newly Diagnosed, Oligo-metastatic Prostate Cancer

Inclusion Criteria: * Have histologically or cytologically diagnosed oligo-metastatic prostate cancer; oligo-metastatic disease is defined to reflect men with low volume disease; specifically, oligo-metastatic disease is defined as less than 5 extra-pelvic metastases; metastatic lesions may be lymph nodes * Be willing and able to provide written informed consent/assent for the trial * Have available tissue from an archival tissue sample or newly obtained core or excisional biopsy of a tumor lesion * Eastern Cooperative Oncology Group (ECOG) performance scale status of 0 or 1 * Demonstrate adequate organ function, all screening labs should be performed within 14 days of treatment initiation * Absolute neutrophil count (ANC) \>= 1,500/mcL * Platelets \>= 100,000/mcL * Hemoglobin \>= 9 g/dL or \>= 5.6 mmol/L * Serum creatinine OR measured or calculated creatinine clearance (glomerular filtration rate \[GFR\] can also be used in place of creatinine or creatinine clearance \[CrCl\]) =\< 1.5 X upper limit of normal (ULN) OR \>= 60 mL/min for subject with creatinine levels \> 1.5 X institutional upper limit of normal (ULN) * Serum total bilirubin =\< 1.5 X ULN OR direct bilirubin =\< ULN for subjects with total bilirubin levels \> 1.5 ULN * 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 * International normalized ratio (INR) or prothrombin time (PT) =\< 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 * 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 anticoagulant * Have testosterone greater than 50 ng/dl * 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 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 * 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 * 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 cervical cancer that has undergone potentially curative therapy * Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis; subjects with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging for at least four weeks prior to the first dose of trial treatment and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases, and are not using steroids for at least 7 days prior to trial treatment * 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; 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 Sjorgen's syndrome will not be excluded from the study * Has evidence of interstitial lung disease or active, non-infectious 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 * Is expecting to father children within the projected duration of the trial, starting with the pre-screening or screening visit through 120 days after the last dose of trial treatment * Has received prior therapy with an anti-PD-1, anti-PD-L1, 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) * Has a known history of human immunodeficiency virus (HIV) (HIV 1/2 antibodies) * Has known active hepatitis B (e.g., hepatitis B 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 severe voiding symptoms (International Prognostic Scoring System \[IPSS\] \> 20) or urinary retention requiring a catheter * Has contraindications to cryotherapy of the prostate, including: previous transurethral prostatic resection (TURP) with persistent transurethral resection (TUR) defect, existing peri-anal or recto-urethral fistula, previous external beam radiation therapy or brachytherapy, coagulopathy, inability to tolerate anesthesia (spinal or general), inability to tolerate transrectal ultrasound (i.e. history of previous abdominal perineal resection)