Pembrolizumab in Treating Patients With Rare Tumors That Cannot Be Removed by Surgery or Are Metastatic

PRIMARY OBJECTIVES: I. To obtain early indication of efficacy by evaluation of non-progression rate (NPR) at 27 weeks as defined as the percentage of patients who are alive and progression-free at 27 weeks as assessed by Response Evaluation Criteria in Solid Tumors (RECIST) version (v)1.1 or immune-related(ir)RECIST or method of tumor evaluation criteria best suitable and accepted for the tumor type evaluated in patients with advanced tumor types receiving pembrolizumab. SECONDARY OBJECTIVES: I. To correlate efficacy by evaluation of tumor size to programmed cell death 1 ligand 1 (PD-L1) status among patients with advanced tumor types receiving pembrolizumab. II. To evaluate safety and tolerability of pembrolizumab in patients with advanced tumors. III. To evaluate the percentage of patients with objective response (complete response \[CR\] or partial response \[PR\]), clinical benefit (CR, PR, or stable disease \[SD\] \>= 4 months), progression free survival (PFS), overall survival (OS), and duration of response (DOR) as assessed by RECIST v1.1 in patients with advanced tumor types receiving pembrolizumab. IV. To evaluate the percentage of patients with objective response (CR or PR), clinical benefit (CR, PR, or SD \>= 4 months), PFS, and DOR as assessed by irRECIST in patients with advanced tumor types receiving pembrolizumab. V. To correlate the NPR at 27 weeks (9 cycles), objective response (CR or PR), clinical benefit CR, PR, or SD \>= 4 months), PFS, OS, and DOR to PD-L1 status among patients with advanced tumor types receiving pembrolizumab. EXPLORATORY OBJECTIVES: I. To evaluate the potential role of tumor-associated immune biomarkers for prediction of therapy effectiveness in patients with advanced tumor types receiving pembrolizumab. II. To correlate the potential role of tumor-associated immune biomarkers for prediction of therapy effectiveness to PD-L1 status among patients with advanced tumor types receiving pembrolizumab. III. To identify imaging characteristics associated with immunological changes in tumor following treatment with pembrolizumab. IV. To compare tumor mutation burden and serial assessment of mutation status in biopsies obtained at baseline and progression in patients with advanced tumor types receiving pembrolizumab. V. To evaluate patient-reported outcomes (PRO) utilizing the National Cancer Institute (NCI) Patient-Reported Outcomes of the Common Terminology Criteria for Adverse Events (PRO-CTCAE) questionnaires. OUTLINE: Patients receive pembrolizumab intravenously (IV) over 30 minutes on day 1. Treatment repeats every 21 days for up to 24 months in the absence of disease progression or toxicity. Patients with clinical response or disease stabilization may continue treatment for up to an additional 12 months. After completion of study treatment, patients are followed up at 30 days and then every 12 weeks.