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 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 chr…