Pembrolizumab in Treating Participants With Leukoplakia

Inclusion Criteria: * Be willing and able to provide written informed consent/assent for the trial. * Subjects must have leukoplakia, erythroleukoplakia or proliferative verrucous leukoplakia (PVL) with lesions measurable in 2 dimensions, not amenable to surgical resection or radiation or who have refused surgery or radiation. Patients must have at least 1 lesion that can be followed on treatment. (Patients who have undergone complete excision of lesions and are clinically without evidence of disease will not be eligible for study.) * Evidence of moderate or severe dysplasia or carcinoma in situ. * Baseline biopsy specimen available for biomarker analysis or willingness to undergo fresh baseline biopsy. * Willingness to consent to photographs of lesions. * Willingness to undergo biopsy at 6 months. * Have a performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG) performance scale. * Absolute neutrophil count (ANC) \>= 1,500 /mcL within 10 days of treatment initiation. * Platelets \>= 100,000/mcL within 10 days of treatment initiation. * Hemoglobin \>= 9 g/dL or \>= 5.6 mmol/L without transfusion or erythropoietin (EPO) dependency (within 7 days of assessment). * Serum creatinine =\< 1.5 X upper limit of normal (ULN) OR measured or calculated creatinine clearance (CrCl) \>= 60 mL/min for subject with creatinine levels \> 1.5 X institutional ULN within 10 days of treatment initiation. (Glomerular filtration rate \[GFR\] can also be used in place of creati…