This phase I trial studies the side effects and best dose of nivolumab when given with ipilimumab in treating patients with human immunodeficiency virus (HIV) associated classical Hodgkin lymphoma that has returned after a period of improvement or does not respond to treatment, or solid tumors that have spread to other places in the body or cannot be removed by surgery. Monoclonal antibodies, such as ipilimumab and nivolumab, may block tumor growth in different ways by targeting certain cells. Ipilimumab is an antibody that acts against a molecule called cytotoxic T-lymphocyte antigen 4 (CTLA-4). CTLA-4 controls a part of your immune system by shutting it down. Nivolumab is a type of antibody that is specific for human programmed cell death 1 (PD-1), a protein that is responsible for destruction of immune cells. Giving ipilimumab with nivolumab may work better in treating patients with HIV associated classical Hodgkin lymphoma or solid tumors.