This phase I/II trial studies the side effects and best dose of duvelisib in combination with nivolumab and to see how well they work in treating patients with stage IIIB-IV melanoma that cannot be removed by surgery (unresectable). Duvelisib is in a class of medications called kinase inhibitors. It works by blocking the signals that cause cancer cells to multiply. This helps to stop the spread of cancer cells. Immunotherapy with monoclonal antibodies, such as nivolumab, may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. Giving duvelisib and nivolumab may help re-sensitize melanoma tumors to respond to anti-PD1 therapy.