Pembrolizumab in Treating Participants With Metastatic, Recurrent or Locally Advanced Cancer and Genomic Instability

PRIMARY OBJECTIVES: I. To evaluate the response rate of pembrolizumab in participants with evidence of genomic instability who have solid tumors with POLE and POLD1 mutations. II. To evaluate the response rate of pembrolizumab in participants with evidence of genomic instability who have solid tumors with BRCA1/2 mutations. SECONDARY OBJECTIVES: I. To compare the complete and partial response rate, and response durability (immune related progression free survival), to historical cohort information of unselected patients treated with pembrolizumab. TERTIARY OBJECTIVES: I. To evaluate the CD4+ and CD8+ T cell response in the tumor microenvironment and peripheral blood of patients treated on this study as well as the frequencies, activation/differentiation, functionality, and co-inhibitory molecule expression of immune cell populations in peripheral blood and tumor, before and after treatment with systemic pembrolizumab. II. To measure PD-L1 expression in pretreatment tumor biopsies and in post treatment tumor tissue, as well as on biopsies taken at progression, to capture data on the relationship between PD-L1 expression and patient outcome. III. To perform deep sequencing for detection of PD-1 and PD-L1 polymorphisms that may correlate with clinical outcomes as well as identification of mutations in immunoregulatory genes that are potential predictors of response to these therapies. IV. To perform exome sequencing of pre-treatment tumor specimens to determine if the presence of immunogenic neoantigens is associated with response. V. To perform ribonucleic acid (RNA) sequencing to determine if expression of checkpoint genes, immune-regulatory modules, or non-coding RNAs including repetitive RNAs and retroelements are associated with response. OUTLINE: Participants receive pembrolizumab intravenously (IV) over 30 minutes on day 1. Courses repeat every 21 days in the absence of disease progression or unacceptable toxicity. Participants with disease progression may continue pembrolizumab for up to 1 year. After completion of study treatment, participants are followed up at 30 days then every 12 weeks.