Brief Summary: This phase I trial investigates the side effects of cabozantinib and nivolumab in treating patients with cancer that may have spread from where it first started to nearby tissue, lymph nodes, or distant parts of the body (advanced) and who are undergoing treatment for human immunodeficiency virus (HIV). Cabozantinib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. 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 cabozantinib and nivolumab may shrink or stabilize cancer in patients undergoing treatment for HIV.

Detailed Description: PRIMARY OBJECTIVES: I. To determine the safety of combined nivolumab and cabozantinib s-malate (XL184 \[cabozantinib\]) in human immunodeficiency virus (HIV) patients with advanced solid tumors. II. To determine the feasibility to deliver the combined nivolumab and XL184 (cabozantinib) for a minimum of 4 cycles in at least 75% of the subjects in the expanded cohort with Kaposi sarcoma (KS) or to achieve a confirmed objective response. SECONDARY OBJECTIVES: I. To observe and record anti-tumor activity in subjects with Kaposi sarcoma (KS). II. To assess the effect of treatment on participants' immune status (CD4 and CD8 cell counts) and HIV viral loads. III. To preliminarily evaluate the objective response rate (ORR) to the combination treatment in subjects with KS. EXPLORATORY OBJECTIVES: I. To assess duration of response (DOR), progression-free survival (PFS), and overall survival (OS) in subjects with KS. II. To assess the PD-L1 immunohistochemistry (IHC) status in tumors and tumor microenvironment and its association with clinical outcome. III. To assess the expression characteristics and cellular distribution of immune checkpoints (PD-L1, B7x, HHLA2, B7H3), infiltrating immune cells (CD4 T cells, CD8 T cells, regulatory T-cells \[Treg\], myeloid-derived suppressor cell \[MDSC\]), and other tumor microenvironment biomarkers (VEGF, VEGFR, MET, and AXL) in the tissue by multiplex quantitative immunofluorescence (MQIF). IV. To correlate markers of immune activation and expansion of immune cell subsets and cytokines with clinical outcomes. V. To assess the treatment effects on latent HIV reservoir. VI. To investigate the dynamic changes of immune checkpoints, angiogenesis markers, and infiltrating immune cells among subjects with available pre- and post-treatment biopsy samples (including subjects with Kaposi sarcoma \[KS\]). OUTLINE: Patients receive cabozantinib s-malate orally (PO) once daily (QD) on days 1-28 of each cycle and nivolumab intravenously (IV) over 30 minutes on day 1 of each cycle. Cycles repeat every 28 days for up to 1 year or 1 year after a partial response is achieved, or 6 months after a complete response is achieved in the absence of disease progression or unacceptable toxicity. Patients also undergo a computed tomography (CT) scan and/or magnetic resonance imaging (MRI) as well as blood sample collection throughout the trial. After completion of study treatment, patients are followed up for 16 weeks.