This phase I trial studies the side effects and best dose of pembrolizumab and recombinant interleukin-12 in treating patients with solid tumors. Immunotherapy with monoclonal antibodies, such as pembrolizumab, may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. Recombinant interleukin-12 may kill tumor cells by blocking blood flow to the tumor and by stimulating white blood cells to kill tumor cells. Giving pembrolizumab and recombinant interleukin-12 may work better than giving pembrolizumab alone in treating patients with solid tumors.