Vemurafenib and Cobimetinib in Treating Patients With BRAF V600E Mutation Positive Craniopharyngioma

* Pre-registration: Patients must have local diagnosis of papillary craniopharyngioma and have tissue slides available for submission to central pathology review; central pathology review will include immunohistochemistry (IHC) testing for BRAF V600E mutation (VE1 clone) and beta-catenin IHC (membranous, non-nuclear pattern) if needed to confirm diagnosis of papillary craniopharyngioma
* Histologically proven papillary craniopharyngioma as documented by central pathology review with positive BRAF V600E mutation by IHC
* Measurable disease and/or non-measurable disease

  * Measurable disease, defined as bidimensionally measurable lesions with clearly defined margins by magnetic resonance imaging (MRI) scans, with a minimum diameter of 10 mm in both dimensions
  * Progressive disease required in cohort B, defined as an increase in the bidirectional area by 25% within the past 13 months after surgery or radiation; progressive or recurrent disease is not required in cohort A, but is allowed provided it is a new diagnosis and patient has not received prior treatment.
* Prior treatment

  * Cohort A: No prior therapy received other than surgery
  * Cohort B: Prior radiation therapy required (any type of prior radiation is allowed)

    * For patients treated with external beam radiation therapy, interstitial brachytherapy or radiosurgery, an interval of \>= 3 months must have elapsed from completion of radiation therapy to registration
    * Recovered to Common Terminology Criteria for Adverse Events (CTCAE) grade 1 or less toxicity attributed to radiation with exception of alopecia, fatigue
  * For patients enrolling on Cohort A or Cohort B:

    * For patients treated with surgery, an interval of \>= 21 days must have elapsed prior to registration
    * No prior treatment with BRAF or MEK inhibitors
    * Steroid dosing stable for at least 4 days prior to registration
* Not pregnant and not nursing; for women of childbearing potential only, a negative pregnancy test done =\< 7 days prior to registration is required
* ECOG performance status =\< 2
* Comorbid conditions

  * No evidence of active bleeding, bleeding diathesis, or hemoptysis (\>= 1/2 teaspoon of red blood) =\< 8 weeks prior to registration
  * No evidence of intracranial hemorrhage =\< 4 weeks prior to registration
  * Patients who have experienced thromboembolic event within 6 months prior to registration must be on stable therapeutic anticoagulation for at least 4 weeks prior to registration
  * No symptomatic congestive heart failure (New York Heart Association class II, III, or IV) within 6 months prior to registration
  * No current unstable angina or uncontrolled arrhythmia
  * No uncontrolled hypertension at time of registration (blood pressure \[BP\] \> 150/95 despite antihypertensive therapy)
  * No known history of prolonged QT syndrome
  * No known history of ventricular arrhythmia within 6 months of registration
  * No known history of uveitis or iritis =\< 4 weeks prior to registration
  * No known history of or evidence of retinal pathology that is considered a risk factor for neurosensory retinal detachment, retinal vein occlusion (RVO), or neovascular macular degeneration within 12 months of registration
  * No known history of chronic lung disease
* Concomitant medications

  * Chronic concomitant treatment with strong CYP3A4 inducers or CYP3A4 inhibitors is not allowed; patients must discontinue the drug at least 14 days prior to study registration
  * Chronic concomitant treatment with CYP1A2 substrate is not allowed; patients must discontinue the drug at least 14 days prior to study registration
* Absolute neutrophil count \>= 1500/mm\^3
* Platelets \>= 100,000/mm\^3
* Creatinine =\< 1.5 mg/dL OR creatinine clearance \>= 45mL/min
* Bilirubin =\< 1.5 upper limit of normal (ULN)
* Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 2.5 ULN