Testing the Use of BRAF-Targeted Therapy After Surgery and Usual Chemotherapy for BRAF-Mutated Colon Cancer

Inclusion Criteria:

* PRE-REGISTRATION (STEP 0) ELIGIBILITY CRITERIA:
* Pre-registration for central tumor testing will occur after colon resection. Pre-registration can occur at any time after surgery through a twelve week period after completion of standard adjuvant therapy
* BRAF V600 mutational status may be determined either locally or by central testing. This testing is mandatory prior to registration to determine eligibility. Tissue submission should be initiated as soon after surgery as possible. For tumors evaluated at local laboratories, formalin-fixed paraffin-embedded (FFPE) tumor tissue must still be submitted for central confirmation of BRAF status
* REGISTRATION (STEP 1) ELIGIBILITY CRITERIA:
* Histologically-proven stage III (any T \[Tx, T1, T2, T3, or T4\], N1-2M0; includes N1C) or high-risk (pT4) stage II colon adenocarcinoma. Tumors must be deemed to originate in the colon including tumors that extend into/involve the small bowel (e.g. those at the ileocecal valve) and must have been completely resected
* BRAF V600E mutation
* MMR proficient (pMMR) or microsatellite stable (MSS) tumor
* Histologic documentation: adenocarcinoma
* Stage: III (any T \[Tx, T1, T2, T3, or T4\], N1-2M0; includes N1C) or high-risk II (pT4)
* Tumor site: colon
* Patients must have received at least 3 months of adjuvant chemotherapy with either leucovorin calcium, fluorouracil, and oxaliplatin (FOLFOX) (minimum of 5 cycles) or capecitabine and oxaliplatin (CAPOX) (minimum of 3 cycles)
* Adjuvant therapy must be completed at most 8 weeks prior to registration
* No other prior medical therapy (chemotherapy, immunotherapy, biologic, or targeted therapy) or radiation therapy for the current colon cancer is permitted
* Not pregnant and not nursing, because this study involves an agent that has known genotoxic, mutagenic and teratogenic effects. Therefore, for women of childbearing potential only, a negative pregnancy test done =\< 7 days prior to registration is required
* Age \>= 18 years
* Eastern Cooperative Oncology Group (ECOG) performance status: 0-2
* Absolute neutrophil count (ANC) \>= 1.0 x 10\^9/L
* Platelet count \>= 75 x 10\^9/L
* Hemoglobin \> 9.0 g/dL
* Total bilirubin =\< 1.5 x upper limit of normal (ULN)
* Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 3.0 x ULN
* Corrected QT (QTc) Interval =\< 480 msec
* Creatinine = calculated (calc.) creatinine clearance \>= 40 mL/min
* No evidence of active and uncontrolled bacterial or viral infection (including active hepatitis B or hepatitis C infection) within 2 weeks prior to start of study intervention; exceptions include:
* Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial

  \* Participants who are hepatitis B surface antigen (HBsAg) negative (-), hepatitis B core antibody (HBcAb) positive (+) are eligible and should be monitored/treated as per local standard of care
* No medical condition such as uncontrolled infection, uncontrolled diabetes mellitus, or cardiac disease which, in the opinion of the treating physician, would make this protocol unreasonably hazardous for the patient
* Patients with known history or current symptoms of cardiac disease or history of treatment with cardiotoxic agents in the last 12 months, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be class 2B or better
* No uncontrolled or poorly-controlled hypertension (\> 180 mmHg systolic or \> 130 mmHg diastolic)
* No history of allergic reactions attributed to compounds of chemical or biologic composition similar to those of cetuximab
* No "currently active" second malignancy other than non-melanoma skin cancers or cervical carcinoma in situ. Patients are not considered to have a "currently active" malignancy if they have completed therapy and are free of disease for \>= 3 years

  * Patients are not considered to have a "currently active" malignancy if they had a gastric or bowel carcinoid \< 1 cm, ductal carcinoma in situ (DCIS)/lobular carcinoma in situ (LCIS) of the breast without invasive cancer, or endometrial dysplasia/carcinoma in situ
  * Patients are not considered to have a "currently active" malignancy if they had a sebaceous neoplasm (sebaceous adenoma, sebaceous epithelioma, sebaceous adenocarcinoma, keratoacanthoma, and squamous cell carcinoma) that was noninvasive
* No known medical condition causing an inability to swallow oral formulations of agents
* No residual Common Terminology Criteria for Adverse Events (CTCAE) version (v) 5.0 grade \>= 2 toxicity from prior chemotherapy, with the exception of grade 2 alopecia or neuropathy
* Drugs that prolong the QTc interval should be avoided if possible, as encorafenib can prolong the QTc interval. Drugs that are generally accepted to have a risk of causing Torsades de Pointes should be discontinued or replaced with drugs that do not carry this risk if at all possible. Patients who receive potential QTc-prolonging medications should be monitored closely
* Chronic concomitant treatment with strong inhibitors of CYP3A4 is not allowed during treatment on this study. Patients on strong CYP3A4 inhibitors must discontinue the drug for 14 days prior to registration on the study
* Chronic concomitant treatment with strong CYP3A4 inducers is not allowed during treatment on this study. Patients must discontinue the drug 14 days prior to registration on the study

Exclusion Criteria: N/A