Trametinib and Trifluridine and Tipiracil Hydrochloride in Treating Patients With Colon or Rectal Cancer That is Advanced, Metastatic, or Cannot Be Removed by Surgery

Inclusion Criteria: * All subjects must have the ability to understand and the willingness to sign a written informed consent * All patients must be able to take oral medications * All patients must be deemed by investigator to have the initiative and means to be compliant with the study protocol (treatment and follow-up) * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Pathologically confirmed advanced, unresectable, or metastatic colon or rectal cancer who have had intolerance to or progression after a fluoropyrimidine, oxaliplatin, irinotecan, and cetuximab or panitumumab in the event of wild-type RAS/BRAF tumors * Of note, prior bevacizumab or regorafenib exposure is not mandated as some patients are deemed poor candidates for anti-angiogenesis therapy and never receive these agents * Tumors must have undergone expanded molecular profiling with a Clinical Laboratory Improvement Act (CLIA)-certified platform that evaluates, at a minimum, RAS, PIK3CA, PTEN and BRAF mutations status * Documented RAS-mutated tumor without activating PIK3CA mutations or PTEN mutation (loss of PTEN or silencing) * Measurable disease by RECIST 1.1 guidelines * Last chemotherapy at least 3 weeks from initiation of study treatment * No investigational agents within 4 weeks from initiation of study treatment * Negative serum or urine beta-human chorionic gonadotropin (HcG) test (female patient of childbearing potential only) performed within 72 hours of prior to first study dose * Absolute neutrophil count (ANC) \>= 1500/mm\^3 (to be performed within 28 days prior to day 1 of protocol therapy) * NOTE: Growth factor is not permitted within 14 days of ANC assessment unless cytopenia is secondary to disease involvement * Platelets \>= 75,000/mm\^3 without transfusions (to be performed within 28 days prior to day 1 of protocol therapy) * Hemoglobin (Hgb) \>= 8 g/dL without transfusions (to be performed within 28 days prior to day 1 of protocol therapy) * Total serum bilirubin \< upper limit of normal (ULN) (to be performed within 28 days prior to day 1 of protocol therapy) * Aspartate aminotransferase (AST) =\< 2.5 x ULN if no liver metastases or =\< 5 x ULN if liver metastases (to be performed within 28 days prior to day 1 of protocol therapy) * Alanine aminotransferase (ALT) =\< 2.5 x ULN if no liver metastases or =\< 5 x ULN if liver metastases (to be performed within 28 days prior to day 1 of protocol therapy) * Creatinine \< 1.5 x ULN or creatinine clearance of \>= 60 mL/min per the Cockcroft-Gault formula (to be performed within 28 days prior to day 1 of protocol therapy) * Female of childbearing potential: negative urine or serum pregnancy test (to be performed within 28 days prior to day 1 of protocol therapy) * If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Corrected QT (QTc) interval =\< 480 ms (12 lead-electrocardiography \[ECG\]) (to be performed within 28 days prior to day 1 of protocol therapy) * Left ventricular ejection fraction \>= 50% as determined by multigated acquisition (MUGA) scan or echocardiogram (to be performed within 28 days prior to day 1 of protocol therapy) * Normal eye examination (to be performed within 28 days prior to day 1 of protocol therapy) * Women of childbearing potential must use highly effective methods of contraception throughout the study and for 4 months after study drug discontinuation * Sexually active men must use a condom during intercourse while taking study drug and for 60 days after study drug discontinuation; a condom is required for vasectomized men to prevent delivery of study drug via seminal fluid Exclusion Criteria: * Prior chemotherapy, biologic, targeted, or radiotherapy within 3 weeks prior to entering study or not recovered from grade \>= 2 adverse events (AEs) due to agents administered more than 4 weeks earlier (except alopecia or neuropathy) * Prior MEK inhibitor or prior TAS-102 therapy * Use of other investigational drugs * History or current evidence of retinal vein occlusion (RVO) or current risk factors for RVO (e.g., uncontrolled glaucoma or ocular hypertension, history of hyperviscosity, or hypercoagulability syndromes) * History of retinal degenerative disease * History of Gilbert's syndrome * Previous or concurrent malignancy with the following exceptions: * Adequately treated basal cell or squamous cell carcinoma of skin with adequate wound healing prior to study entry * In situ carcinoma of the cervix treated curatively and without evidence of recurrence * Primary malignancy completely resected and in complete remission \>= 1 year * History of acute coronary syndromes (including myocardial infarction, unstable angina, coronary artery bypass graft, coronary angioplasty, or stenting) \< 6 months prior to screening * Impaired cardiovascular function or clinically significant cardiovascular disease including any of the following: symptomatic congestive heart failure, clinically significant cardiac arrhythmias and/or conduction abnormalities \< 6 months prior to screening except for atrial fibrillation and paroxysmal supraventricular tachycardia * Uncontrolled arterial hypertension despite appropriate medical therapy (systolic blood pressure \> 160 or diastolic blood pressure \> 100) * Neuromuscular disorders associated with elevated creatine kinase (CK, e.g., inflammatory myopathies, muscular dystrophy, amyotrophic lateral sclerosis, or spinal muscular atrophy) * Started or planning to start on strenuous exercise regimen after first dose of study treatment (i.e., muscular activities, such as strenuous exercise, that can result in significant increase in plasma CK levels should be avoided while on trametinib treatment) * Gastrointestinal (GI) disease or impairment of GI function (e.g., active ulcerative disease, uncontrolled nausea, vomiting, or diarrhea, malabsorption syndrome, or small bowel resection) * Prior major surgery =\< 3 weeks before study drug or not recovered from side effects of such procedure * Ongoing grade \>= 3 neuropathy * Known hypersensitivity to any components of study drugs * Prior intolerance to a fluoropyrimidine * Any other condition that would, in the investigator's judgement, contraindicate the patient's participation in the clinical study due to safety concerns with clinical study procedures (e.g., infection/inflammation, intestinal obstruction, unable to swallow medications, social/psychological issues, etc.) * Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)