Testing the Addition of an Anti-Cancer Drug, Abemaciclib, to the Usual Chemotherapy Treatment (5-Fluorouracil) for Metastatic, Refractory Colorectal Cancer

Inclusion Criteria: * Patients must have histologically or cytologically confirmed microsatellite stability (MSS) metastatic colorectal cancer where patients have progressed on standard therapies which would have included 5-FU or capecitabine, oxaliplatin, and irinotecan. Patients must have had progression of disease (PD) or intolerance to bevacizumab and anti-EGFR antibodies (cetuximab or panitumumab) in patients who have left-sided and RAS-wildtype colorectal cancer (CRC) * Patients must have measurable disease * Age ≥ 18 years. Because no dosing or adverse event data are currently available on the use of abemaciclib in combination with 5-FU in patients \< 18 years of age, children are excluded from this study * Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2 (Karnofsky ≥ 60%) * Hemoglobin ≥ 8 g/dL * Absolute neutrophil count ≥ 1,500/mcL * Platelets ≥ 100,000/mcL * Total bilirubin ≤ 1.5 x institutional upper limit of normal (ULN) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/ alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) ≤ 3 x institutional ULN for patients who do not have liver metastases, and ≤ 5 x institutional ULN for patients with liver metastases * Glomerular filtration rate (GFR) ≥ 50 mL/min/1.73 m\^2 * Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial * For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated * Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load * Patients with treated brain metastases are eligible if follow-up brain imaging after central nervous system (CNS)-directed therapy shows no evidence of progression * Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial * Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, 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 II or better * Patients must have available archival tumor tissue at the time of patient enrollment for molecular profiling studies. A biopsy may be done if archival tissue is not available * Palliative radiation for symptom management to a metastatic site will be permitted during the course of the study. Please discuss specific cases with the national principal investigator (PI) * Patients must have completed previous systemic therapy for at least five half-lives or 2 weeks, whichever is shorter, prior to study dosing * Patients who have not had major surgery within 14 days prior to randomization * Patients who do not have serious and/or uncontrolled preexisting medical condition(s) that, in the judgment of the investigator, would preclude participation in this study (for example, interstitial lung disease, severe dyspnea at rest or requiring oxygen therapy, severe renal impairment \[e.g. estimated creatinine clearance \< 30ml/min\], history of major surgical resection involving the stomach or small bowel, or preexisting Crohn's disease or ulcerative colitis or a preexisting chronic condition resulting in baseline grade 2 or higher diarrhea) * Patients who received radiotherapy must have completed and fully recovered from the acute effects of radiotherapy. A washout period of at least 14 days is required between end of radiotherapy and randomization * Patients who are able to swallow oral medications * Patients who do not have a personal history of any of the following conditions: syncope of cardiovascular etiology, ventricular arrhythmia of pathological origin (including, but not limited to, ventricular tachycardia and ventricular fibrillation), or sudden cardiac arrest * Patients who do not have an active systemic bacterial infection (requiring intravenous \[IV\] antibiotics at time of initiating study treatment) or fungal infection * The effects of abemaciclib on the developing human fetus are unknown. For this reason and because cyclin-dependent kinases (CDK) inhibiting agents as well as other therapeutic agents used in this trial are known to be teratogenic, men and women treated or enrolled on this protocol must also agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to the study, for the duration of study participation, and 3 months after completion of abemaciclib and fluorouracil. 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 * Ability to understand and the willingness to sign a written informed consent document. Legally authorized representatives may sign and give informed consent on behalf of study participants Exclusion Criteria: * Patients who have not recovered from adverse events due to prior anti-cancer therapy (i.e., have residual toxicities \> grade 1) with the exception of alopecia or grade 2 peripheral neuropathy. Patients who are experiencing immune related adverse events (AEs) which are adequately treated with hormone replacement therapy, including diabetes on insulin regimen, hypothyroidism on levothyroxine, and adrenal insufficiency on steroid replacement will also be eligible * Patients who are receiving any other investigational agents. There is to be a washout period of two weeks or five half-lives, whichever is shorter, for all investigational agents prior to treatment initiation on this study. Individual cases can be discussed with the national PI * History of allergic reactions attributed to compounds of similar chemical or biologic composition to abemaciclib or other agents (5-FU) used in study such as a previous intolerance to 5-FU or capecitabine, including patients with known or suspected dihydropyrimidine dehydrogenase deficiency * Patients who have received previous treatment with a CDK4/6 inhibitor * Patients with a gastrointestinal pathology or history that adversely impacts the ability to take or absorb oral medication * Patients with peritoneal metastases complicated by ascites which are refractory to diuretic therapy and requires therapeutic paracenteses more than once every 2 weeks * Patients receiving any medications or substances that are strong inhibitors or inducers of CYP3A enzymes before enrollment or while on protocol therapy are ineligible. Patients receiving moderate CYP3A inhibitors or inducers will be monitored. Because the lists of these agents are constantly changing, it is important to regularly consult a frequently-updated medical reference. As part of the enrollment/informed consent procedures, the patient will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the patient is considering a new over-the-counter medicine or herbal product * Patients with uncontrolled intercurrent illness or any other significant condition(s) that would make participation in this protocol unreasonably hazardous * Pregnant women are excluded from this study because abemaciclib is a CDK-inhibiting agent with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with abemaciclib, breastfeeding should be discontinued if the mother is treated with abemaciclib. These potential risks may also apply to other agents used in this study