Dabrafenib and Trametinib Before and After Surgery in Treating Patients With Stage IIIB-C Melanoma With BRAF V600 Mutation

Inclusion Criteria: * Capable of giving written informed consent, which includes compliance with the requirements and restrictions listed in the consent form * Patients must have histologically or cytologically confirmed stage IIIB/C melanoma by American Joint Committee on Cancer (AJCC) version 7; the definition of resectability can be determined by the patient's surgical oncologist and verified via discussion at Multidisciplinary Tumor Conference attended by melanoma medical and surgical oncology staff; resectable tumors are defined as having no significant vascular, neural or bony involvement; only cases where a complete surgical resection with tumor-free margins can safely be achieved are defined as resectable * Multicenter sites: confirmation of diagnosis via histology or cytology will be made by the local site pathologist; likewise, resectability determination will be made by the site's multidisciplinary team * Patients must be medically fit enough to undergo surgery as determined by the surgical oncology team * BRAF mutation-positive melanoma (V600E or V600K) based on report from a Clinical Laboratory Improvement Amendments (CLIA) certified laboratory * Patients must have measurable disease, defined by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 * Eastern Cooperative Oncology Group (ECOG) performance status 0-1 * Absolute neutrophil count (ANC) \>= 1.5 x 10\^9/L * Hemoglobin \>= 9.5 g/dL * Platelets \>= 100 x 10\^9/L * Prothrombin time/international normalized ratio (PT/INR) and partial thromboplastin time (PTT) =\< 1.5 x upper limit of normal (ULN) * Total bilirubin =\< 1.5 x ULN (isolated bilirubin \> 1.5 x ULN is acceptable if bilirubin is fractionated and direct bilirubin \< 35%) * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 2.5 x ULN * Albumin \>= 2.5 g/dL * Creatinine =\< 1.5 x ULN OR calculated creatinine clearance \>= 50 mL/min OR 24-hour urine creatinine clearance \>= 50 mL/min * Male subjects must agree to use one of the contraception methods listed below; this criterion must be followed from the time of the first dose of study medication until 4 weeks after the last dose of study medication; however, it is advised that contraception be used for a total of 16 weeks following the last dose (based on the lifecycle of sperm); methods: a) abstinence, defined as sexual inactivity consistent with the preferred and usual lifestyle of the subject; periodic abstinence (e.g. calendar, ovulation, symptothermal, post-ovulation methods) and withdrawal are not acceptable methods of contraception; b) condom (during non-vaginal intercourse with any partner - male or female) OR c) condom and occlusive cap (diaphragm or cervical/vault caps) plus spermicidal agent (foam/gel/film/cream/suppository) (during sexual intercourse with a female) * A female subject is eligible to participate if she is of: * Non-childbearing potential defined as pre-menopausal females with a documented tubal ligation or hysterectomy; or postmenopausal defined as 12 months of spontaneous amenorrhea (in questionable cases a blood sample with simultaneous follicle stimulating hormone \[FSH\] \> 40 MlU/mL and estradiol \< 40 pg/mL \[\< 140 pmol/L\] is confirmatory); females on hormone replacement therapy (HRT) and whose menopausal status is in doubt will be required to use one of the contraception methods listed below if they wish to continue their HRT during the study; otherwise, they must discontinue HRT to allow confirmation of post-menopausal status prior to study enrollment; for most forms of HRT, at least 2-4 weeks will elapse between the cessation of therapy and the blood draw; this interval depends on the type and dosage of HRT; following confirmation of their post-menopausal status, they can resume use of HRT during the study without use of a contraceptive method * Child-bearing potential and agrees to use one of the contraception methods listed below for an appropriate period of time (as determined by the product label or investigator) prior to the start of dosing to sufficiently minimize the risk of pregnancy at that point; female subjects must agree to use contraception until 4 weeks after the last dose of study medication, and must have a negative serum or urine pregnancy test within 14 days prior to the start of dosing * Female subjects contraception methods: a) abstinence; b) intrauterine device (IUD) or intrauterine system (IUS) that meets the \< 1% failure rate as stated in the product label; c) male partner sterilization prior to the female subject's entry into the study, and this male is the sole partner for that subject; d) double barrier method: condom and occlusive cap (diaphragm or cervical/vault caps) plus spermicidal agent (foam/gel/film/cream/suppository) Exclusion Criteria: * Currently receiving cancer therapy (chemotherapy, radiation therapy, immunotherapy, or biologic therapy) or investigational anti-cancer drug within 28 days * Current use of a prohibited medication or requires any of these medications during treatment with study drug * Prior BRAF or mitogen-activated protein kinase kinase (MEK) directed therapy * Prior malignancy except for the following: adequately treated basal cell or squamous cell skin cancer, in-situ cervical cancer, thyroid cancer (except anaplastic) or any cancer from which the patient has been disease-free for 2 years * Any major surgery within the last 3 weeks * History of central serous retinopathy (CSR) or retinal vein occlusion (RVO), or predisposing factors to RVO or CSR (e.g. uncontrolled glaucoma or ocular hypertension, uncontrolled systemic disease such as hypertension, diabetes mellitus, or history of hyperviscosity or hypercoagulability syndromes) * Presence of active gastrointestinal disease or other condition that will interfere significantly with the absorption, distribution, metabolism, or excretion of drugs * Brain metastases or bone metastases; patients with brain metastases must have received treatment for them (resection or stereotactic radiosurgery \[SRS\]) and these metastatic foci must be stable for 8 weeks prior to starting study drug * Corrected QT (QTc) interval \>= 480 msec (\>= 500 msec for subjects with bundle branch block) * Uncontrolled arrhythmias * Class II, III, or IV heart failure as defined by the New York Heart Association (NYHA) functional classification system * Pregnant or lactating female * Unwillingness or inability to follow the procedures required in the protocol * Uncontrolled diabetes, hypertension or other medical conditions that may interfere with assessment of toxicity * Subjects with known glucose 6 phosphate dehydrogenase (G6PD) deficiency