Testing Dabrafenib and Trametinib With or Without Hydroxychloroquine in Stage IIIC or IV BRAF V600E/K Melanoma

This phase II trial investigates how well adding hydroxychloroquine to the standard treatment of dabrafenib and trametinib works to overcome resistance and delay disease progression in treating patients with stage IIIC or IV BRAF V600E/K melanoma. Hydroxychloroquine may cause cell death in tumor cells that rely on a process called \"autophagy\" for survival. Dabrafenib and trametinib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Giving hydroxychloroquine together with dabrafenib and trametinib may work better than dabrafenib and trametinib alone to shrink and stabilize the cancer.