The purpose of this study is to determine the effectiveness of combining immune therapy, pembrolizumab, with a hypomethylating agent, azacitidine, for pancreatic cancer. People who have advanced pancreatic cancer with disease progression on first-line therapy are usually treated with a second chemotherapy regimen. However, there is no single accepted chemotherapy regimen and national guidelines recommend chemotherapy or clinical trial participation. In this study, all study subjects will receive a combination of immune therapy (every 3 weeks) and a hypomethylating agent (every 4 weeks).To date, studies have shown that combining a hypomethylating agent with chemotherapy or immune therapy may benefit patients across different solid tumor types including pancreatic cancer. Preclinical data in a mouse model of pancreatic cancer demonstrates improvement in survival with the combination of a hypomethylating agent and immune therapy. However, the use of single agent hypomethylating agent or immune therapy has not been shown to be effective in patients with pancreatic cancer. The one exception, to date, is the use of immune therapy in those individuals with a particular genetic feature known as mismatch repair deficiency and microsatellite instability. The combination of immune therapy and a hypomethylating agent has not been studied in human subjects and is not approved by the FDA for use in pancreatic cancer.