Dabrafenib and Pazopanib Hydrochloride in Treating Patients With Advanced Malignant Tumors

Inclusion Criteria: * Must have a histologically or cytologically confirmed malignant tumor that is advanced, metastatic or unresectable and for which standard curative or palliative measures do not exist or are no longer effective * Tumors must carry the BRAF mutation * Prior therapies: * There is no limit to prior cytotoxic regimens * No more than three prior regimens of tyrosine kinase inhibitors are allowed; prior use of pazopanib and/or inhibitor dabrafenib is not allowed; prior use of vemurafenib and sorafenib is allowed * Patients must not have received systemic chemotherapy, immunotherapy, biologic therapy or radiation therapy within 4 weeks of study * Adverse events related to prior tumor-specific therapy must have been resolved to =\< grade 1 prior to study enrollment except for alopecia * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Life expectancy greater than 12 weeks * Absolute neutrophil count (ANC) \>= 1.5 X 10\^9/L; for patients (pts) with hairy cell leukemia, ANC \>= 1 X 10\^9/L is required * Hemoglobin \>= 9 g/dL (5.6 mmol/L); for pts with hairy cell leukemia, hemoglobin \>= 8 g/dL is required * Platelets \>= 100 X 10\^9/L; for pts with hairy cell leukemia, platelets \>= 75 X 10\^9/L is required * International normalized ratio (INR) =\< 1.2 X upper limit of normal (ULN); subjects receiving anticoagulant therapy with warfarin are not eligible * Activated partial thromboplastin time (aPTT) =\< 1.2 X ULN * Total bilirubin =\< 1.5 X ULN; concomitant elevations in bilirubin and aspartate aminotransferase (AST)/alanine aminotransferase (ALT) above 1.0 x ULN are not permitted * ALT and AST =\< 2.5 X ULN; concomitant elevations in bilirubin and AST/ALT above 1.0 x ULN are not permitted * Serum creatinine =\< 1.5 x ULN (=\< 133 umol/L) * Urine protein to creatinine ratio (UPC; appropriate) \< 1; if UPC \>= 1, then a 24-hour urine protein must be assessed; subjects must have a 24-hour urine protein value \< 1 g to be eligible; use of urine dipstick for renal function assessment is not acceptable * Left ventricular ejection fraction \>= institutional lower limit of normal * The effects of dabrafenib on the developing human fetus are unknown; pazopanib belongs to the pregnancy risk factor group D (adverse effects were observed in animal studies); for these reasons, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately; men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of dabrafenib and pazopanib administration * Ability to understand and willingness to sign a written informed consent document * Ability to swallow oral medication and keep a pill diary Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks prior to study enrollment * Patients who are receiving any other investigational agents * Patients with symptomatic, untreated brain metastases; patients who are on a stable dose of corticosteroids for more than 1 month or off corticosteroids for 2 weeks can be enrolled; enzyme-inducing anti-epileptic drugs are not permitted; screening with central nervous system (CNS) imaging (computerized tomography \[CT\] or magnetic resonance imaging \[MRI\]) is required only if clinically indicated * Patients with a known history of glucose-6-phosphate dehydrogenase (G6PD) deficiency; patients with G6PD deficiency are excluded from clinical trials because they may develop nonimmune hemolytic anemia in response to dabafenib, which contains a sulfonamide, a potential risk factor for subjects with this deficiency * Patients taking prohibited medications within 7 days of entering study will be excluded due to potential serious interactions with dabafenib; patients taking therapeutic doses of warfarin will not be allowed on the study due to potential drug interactions (patient on prophylactic low dose warfarin are allowed) * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study because dabrafenib is an investigational agent with unknown teratogenicity and because pazopanib belongs to pregnancy risk factor group D (adverse effects were observed in animal studies); because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with dabrafenib and pazopanib, breastfeeding should be discontinued if the mother is treated with these agents * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are excluded because of possible pharmacokinetic interactions of highly active anti-retroviral therapy (HAART) with dabrafenib and pazopanib; in addition, these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy; appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated * Poorly controlled hypertension (defined as systolic blood pressure \[BP\] \>= 140 and/or diastolic BP \>= 90) measured on more than one occasion and not responsive to antihypertensives; Note: Initiation or adjustment of antihypertensive medication(s) is permitted prior to study entry and during study if required; BP must be re-assessed on two occasions separated by a minimum of 1 hour; on each of these occasions, the mean systolic (S)BP/diastolic (D)BP values (of 3 readings) must be \< 140/90 mmHg in order for a subject to be eligible for the study * Prolongation of heart rate-corrected QT interval (QTc) \> 480 msecs (using Bazett's formula) * History of at least one of the following cardiovascular conditions within the past 6 months: * Cardiac angioplasty or stenting * Myocardial infarction * Unstable angina * Symptomatic peripheral vascular disease * Class III or IV congestive heart failure, as defined by the New York Heart Association * History of valvular dysfunction on echocardiogram excluding mild valvular dysfunction * Known cardiac metastasis * History of cerebrovascular accident including transient ischemic attack (TIA), pulmonary embolism or untreated deep venous thrombosis (DVT) within the past 6 months; patients who are being treated for pulmonary embolism (PE) and/or DVT diagnosed within the past 6 months with agents other than warfarin are allowed to enter the study * Prior major surgery or trauma within 28 days before first dose of study drug and/or presence of any non-healing wound, fracture, or ulcer * Evidence of active bleeding or bleeding diathesis * Patient with hepatitis B and/or hepatitis C infection; patients with laboratory evidence of hepatitis B virus (HBV) clearance are eligible for the trial * Patient with history of malignancy other than completely resected non-melanomatous skin carcinoma or successfully treated in situ carcinoma within 5 years of study enrollment * Clinically significant gastrointestinal abnormalities that may affect absorption of the study drugs including but not limited to: * Malabsorption syndrome * Major resection of the stomach or small bowel