Testing Trametinib and Dabrafenib as a Potential Targeted Treatment in Cancers With BRAF Genetic Changes (MATCH-Subprotocol H)

Inclusion Criteria: * Patients must have met applicable eligibility criteria in the Master MATCH Protocol prior to registration to treatment subprotocol * Patients must have a BRAF V600E or, V600K, V600R or V600D mutation, or another aberration, as identified via the MATCH Master Protocol * Prothrombin time (PT)/International normalized ratio (INR) and partial thromboplastin time (PTT) =\< 1.3 x institutional ULN; subjects receiving anticoagulation treatment may be allowed to participate with INR established within the therapeutic range prior to registration to treatment * Patients must have an ECHO or a nuclear study (multigated aquisition scan \[MUGA\] or First Pass) within 4 weeks prior to registration to treatment and must not have a left ventricular ejection fraction (LVEF) \< the institutional lower limit of normal (LLN). If the LLN is not defined at a site, the LVEF must be \> 50% for the patient to be eligible * Patients must have an electrocardiogram (ECG) within 8 weeks prior to treatment assignment and must have NONE of the following cardiac criteria: * Clinically important abnormalities in rhythm, conduction or morphology of resting ECG (e.g. complete left bundle branch block, third degree heart block) * Treatment-refractory hypertension defined as a blood pressure of systolic \> 140 mmHg and/or diastolic \> 90 mmHg which cannot be controlled by anti-hypertensive therapy * Patients who previously received monoclonal antibody therapy (eg. ipilimumab and others) must have stopped the prior therapy for 8 or more weeks before starting on trametinib and dabrafenib Exclusion Criteria: * Patients with a diagnosis of metastatic melanoma from a cutaneous, acral, mucosal, or unknown primary site are excluded * Patients with a diagnosis of papillary thyroid cancer are excluded * Patients with a diagnosis of colorectal adenocarcinoma are excluded * Patients with a diagnosis of non-small cell lung cancer are excluded * Patients with a history of interstitial lung disease or pneumonitis are excluded * Patients must not have known hypersensitivity to dabrafenib and trametinib or compounds of similar chemical or biologic composition or to dimethyl sulfoxide (DMSO) * Patients must not have a history or current evidence/risk of retinal vein occlusion (RVO). An eye exam is required at baseline * Patients who previously received MEK inhibitors (including, but not limited to, trametinib, binimetinib, cobimetinib, selumetinib, RO4987655 (CH4987655), GDC-0623 and pimasertib) will be excluded * Patients who previously received BRAF inhibitors (including, but not limited to, dabrafenib (Tafinlar), vemurafenib (PLX-4720) (Zelboraf), RAF265, LGX818 (encorafenib), RO5212054 (PLX3603), ARQ 736, XL281 (BMS-908662), CEP-32496, and the BRAF/MEK dual inhibitor (RO5126766) will be excluded * Patients with prior exposure to dabrafenib or trametinib on another treatment subprotocol of the MATCH trial are excluded * Current use of a prohibited medication. Patients receiving any medications or substances that are strong inhibitors or inducers of CYP3A or CYP2C8 are ineligible. Current use of, or intended ongoing treatment with: herbal remedies (e.g., St. John's wort), or strong inhibitors or inducers of P-glycoprotein (Pgp) or breast cancer resistance protein 1 (Bcrp1) should also be excluded * Patients with a history of hepatitis B virus (HBV) or hepatitis C virus (HCV) infection are excluded. An exception will be patients with cleared HBV and HCV infection which will be allowed on study * Patients with history of RAS mutation-positive tumors are not eligible regardless of interval from the current study * NOTE: Prospective RAS testing is not required. However, if the results of previous RAS testing are known, they must be used in assessing eligibility