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

Patient must have locally advanced unresectable stage IIIC or stage IV melanoma

Patient must have BRAF V600E or BRAF V600K tumor genotype based on a Clinical Laboratory Improvement Act (CLIA) approved assay

Patient must have serum LDH \> Upper limit of normal per institution standards

Patient must have measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1. Baseline measurements of sites of disease must be obtained within 3 weeks prior to study randomization

Patient must have been treated with prior immune checkpoint inhibitor therapy (anti PD-1 antibody, anti-CTLA-4 antibody or a combination regimen including either or both agents) either in the adjuvant or metastatic setting. Patient may have received investigational agents in combination with standard therapy, as long as it was adhering to the timeframes below

* Patient must have discontinued active immunotherapy (IL-2, interferon, anti-CTLA-4 antibody, anti-PD-1 antibody etc.) or chemotherapy at least 4 weeks prior to randomization

* Patient must have discontinued any oral targeted therapy at least 2 weeks prior to randomization

Patient may have been treated with prior chemotherapy or radiation therapy

Patient must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1

Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial

All females of childbearing potential must have a blood test or urine study within 14 days prior to randomization to rule out pregnancy.

Women of childbearing potential and sexually active males must not expect to conceive or father children by using accepted and effective method(s) of contraception or abstaining from sexual intercourse for the duration of their participation in the study and for 4 months after the last dose of protocol treatment

Patient must have recovered from clinically significant reversible toxicities from previous treatment prior to randomization. Abnormal laboratory values may be grade 1, as long as they meet the eligibility criteria for organ and marrow function

Patient must be able to swallow and retain oral medication and must not have any clinically significant gastrointestinal abnormalities that may alter absorption such as malabsorption syndrome or major resection of the stomach or bowels

Patient must have the ability to understand and the willingness to sign a written informed consent document. Patients with impaired decision-making capacity (IDMC) who have a legally authorized representative (LAR) or caregiver and/or family member available will also be considered eligible

Absolute neutrophil count \>= 1,500/mcL (obtained =\< 14 days prior to protocol randomization)

Platelets \>= 100,000/mcL (obtained =\< 14 days prior to protocol randomization)

Total bilirubin =\< institutional upper limit of normal (ULN) (obtained =\< 14 days prior to protocol randomization)

Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3.0 x institutional ULN (obtained =\< 14 days prior to protocol randomization)

Creatinine =\< 1.5 x institutional ULN (obtained =\< 14 days prior to protocol randomization)

Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial

For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated

* NOTE: Patient with treated brain metastases are eligible. No brain imaging is required, however, 1 week must elapse after gamma knife therapy. Patient treated with whole brain radiation that have been stable for 2 months are eligible. Patient are excluded if they have leptomeningeal disease or metastases causing spinal cord compression that are symptomatic or untreated or not stable (documented by imaging) for at least 3 months or requiring corticosteroids. Patients on a stable dose of corticosteroids for at least 1 month or who have been off of corticosteroids for at least 1 week are eligible

What this study is about