Pembrolizumab and Vorinostat in Treating Patients With Recurrent Squamous Cell Head and Neck Cancer or Salivary Gland Cancer That Is Metastatic and/or Cannot Be Removed by Surgery

This phase I/II trial studies the side effects of pembrolizumab and vorinostat in treating patients with squamous cell head and neck cancer or salivary gland cancer that has come back, has spread to other places in the body and/or cannot be removed by surgery. Monoclonal antibodies, such as pembrolizumab, may interfere with the ability of tumor cells to grow and spread. Vorinostat may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Giving pembrolizumab together with vorinostat may be a better treatment for head and neck cancer or salivary gland cancer.