Recurrent Pharyngeal Squamous Cell Carcinoma

This phase I trial is to find out the possible side effects of pembrolizumab and radiation therapy before and during surgery in treating patients with head and neck squamous cell cancer that remains despite treatment (persistent) or has come back (recurrent). 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. Radiation therapy uses high energy x-rays or protons to kill tumor cells and shrink tumors. Giving pembrolizumab and radiation therapy before and during surgery may kill more tumor cells.