Dabrafenib Alone and in Combination With Trametinib Before Surgery in Treating Patients With Locally or Regionally Advanced Melanoma That Can Be Removed By Surgery

Inclusion Criteria: * Signed written informed consent * Patients with locally-or regionally advanced melanoma being considered for resection of the lesion(s) for local-regional control and potential cure * Patients with limited, resectable metastatic disease (three or fewer lesions) are eligible if surgical resection is considered to be the best therapeutic option * Patients with AJCC clinical stage IIb-IV disease at initial diagnosis, or patients with melanoma of any stage with advanced local or regional recurrence, with or without limited resectable metastatic disease, would be eligible * B-RAF V-600 mutation positive by snapshot molecular analysis * Individuals with B-RAF V-600 mutations other than V600E are eligible * Measurable disease, i.e. presenting with at least one measurable lesion per Response Evaluation Criteria in Solid tumors (RECIST) 1.1 * All prior treatment related toxicities must be Common Terminology Criteria for Adverse Events (CTCAE) (Version 4.0) =\< Grade 1 at the time of enrollment * Adequate baseline organ function defined by the criteria below: * Absolute Neutrophil Count (ANC) \>= 1.5 X 10\^9/L * Platelet Count \>= 60 X 10\^9/L * Hemoglobin \>= 9 g/dl * Creatinine =\< 2 mg/dl * Aspartate aminotransferase (AST) =\< 100 U/L * Alanine aminotransferase (ALT) =\< 100 U/L * Alkaline Phosphatase =\< 380 U/L * Total Bilirubin =\< 2.0 mg/dl * Women of childbearing potential must have a negative serum pregnancy test within 14 days of first dose of study treatment and agree to use effective contraception during the study and for 7 days following the last dose of study treatment * Men with a female partner of childbearing potential must have either had a prior vasectomy or agree to use effective contraception from 1 day prior to administration of the first dose of study treatment until 7 days after the last dose of study treatment Exclusion Criteria: * ECOG Performance Status \> 2 * Lactating female * Any serious and/or unstable pre-existing medical, psychiatric disorder, or other conditions that could interfere with subject's safety, obtaining informed consent or compliance to the study procedures * Any serious medical condition that would render the patient unable to undergo surgical resection or would limit life expectancy to less than 1 year * Any prohibited medication * Administration of an investigational drug within 30 days or 5 half-lives, whichever is longer, preceding the first dose of study treatment * A known immediate or delayed hypersensitivity reaction or idiosyncrasy to drugs chemically related to GSK-2118436 (dabrafenib) or GSK-1120212 (trametinib) or excipient that contraindicates their participation * Patients with a history of severe cardiovascular disease as defined: * Symptomatic or uncontrolled cardiac arrhythmias * Treatment refractory hypertension, defined as a systolic blood pressure \> 160mm Hg and/or diastolic \> 100 mmHg which cannot be controlled by antihypertensive therapy. * Current ≥ NYHA Class II congestive heart failure * History of myocardial infarction or unstable angina within 6 months prior to study entry. * History of stroke or TIA within 6 months prior to study entry * QTc ≥ 480 msec * Cardiac valvular disease ≥ grade 2. * Patients with a history of interstitial lung disease or interstitial pneumonitis * A history of known Human Immunodeficiency Virus (HIV), Hepatitis B Virus (HBV), or Hepatitis C Virus (HCV) infection. * History of another active malignancy within the past 5 years, or any malignancy with a confirmed activating RAS mutation. Please note that prospective RAS mutation testing is not required, however, if results of previous RAS testing are known, they must be used in assessing eligibility. Subjects with a history of completely resected non-melanoma skin cancer are eligible. * A history or current evidence/risk of retinal vein occlusion (RVO) or CSR including: * a. Presence of predisposing factors to RVO or CSR (e.g., uncontrolled glaucoma or ocular hypertension, uncontrolled hypertension, uncontrolled diabetes mellitus, or a history of hyperviscosity or hypercoagulability syndromes); or * b. Visible retinal pathology as assessed by ophthalmic examination that is considered a risk factor for RVO or CSR such as: * i. Evidence of new optic disc cupping; * ii. Evidence of new visual field defects on automated perimetry; * iii. Intraocular pressure \>21 mmHg as measured by tonography.