TAS-102 With Concurrent Radiation for the Treatment of Untreated Resectable Stage II-III Rectal Cancer

Inclusion Criteria: * All races and ethnic groups will be included * Histologically confirmed diagnosis of adenocarcinoma of the rectum * Clinical stage II (T3-4aN0M0) and stage III (T1-4aN1+M0) based on MRI * Resectable primary rectal tumor at baseline * No evidence of distant metastases * No prior pelvic radiation therapy * No prior chemotherapy or surgery for rectal cancer * No active infections requiring systemic antibiotic treatment (oral antibiotics are acceptable at the discretion of the treating physician) * Eastern Cooperative Oncology Group (ECOG) performance status 0-1 * Leukocytes \>= 3,000/uL * Absolute neutrophil count \>= 1,500/uL * Hemoglobin \>= 9.0 gm/dL * Platelets \>= 100,000/uL * Total bilirubin within normal institutional limits * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional upper limit of normal (ULN) * Creatinine within normal institutional limits, OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for participants with creatinine levels above institutional normal * Female participants of childbearing potential must have a negative urine or serum pregnancy test within 7 days prior to receiving the first dose of study medication. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. A female of childbearing potential is defined of one who is biologically capable of becoming pregnant. Reliable contraception should be used starting from trial screening and must be continued throughout the study * Females of childbearing potential must agree to use effective contraceptive method starting with the first dose of study therapy through 6 months after the last dose of study therapy * Male participants must agree to use an effective method of contraception starting with the first dose of study therapy through 6 months after the last dose of study therapy * Participants must read, have the ability to understand, agree to, and sign a statement of Informed Consent prior to participation in this study * Participants must, as part of their planned treatment per institutional guidelines, be: * Scheduled to receive preoperative FOLFOX or CAPOX chemotherapy, which requires a central venous access device for administration * Able to undergo planned TME of the rectal tumor per institutional standards Exclusion Criteria: * Recurrent rectal cancer * Primary unresectable rectal cancer. A tumor is considered unresectable when invading adjacent organs (T4b disease) and an en bloc resection will not achieve negative margins. Rectal cancer presenting with concurrent or overlapping sites in the colon is eligible if these sites could be removed with surgery * Distant nodal disease (retroperitoneal nodes), or any metastatic disease by computed tomography (CT) or positron emission tomography (PET) * Creatinine \> 1.5 x ULN * History of peripheral neuropathy \> grade 2 * History of malabsorption syndromes or inflammatory bowel disease * Use of immunosuppressive or myelosuppressive medications including but not limited to adalimumab, azathioprine, BCG, clozapine, cyclosporine, deferiprone, etanercept, fingolimod, hydroxyurea, interferon, leflunomide, methotrexate, mycophenolate, natalizumab, pimecrolimus, rituximab, sirolimus, and tacrolimus * Inability to take oral medications * Participants who received prior pelvic radiotherapy * Use of induction chemotherapy prior to chemo-radiation of rectal cancer * Use of other chemotherapy regimens other than FOLFOX or CAPOX * Participants who are unable to undergo an MRI * Participants who are unable to undergo TME * Refusal of standard-of-care TME of the rectal tumor if there is persistent disease after neoadjuvant treatment * Participants with a history of any arterial thrombotic event within the past 6 months, including angina (stable or unstable), myocardial infarction (MI), transient ischemic attack (TIA), or cerebrovascular accident (CVA) * Participants with a recent history of venous thrombotic episodes such as deep venous thrombosis and pulmonary embolism within the past 3 months. If these episodes occurred more than three months prior to enrollment, they may be considered for protocol participation, provided they are on stable doses of anticoagulant therapy. Similarly, participants who are anticoagulated for atrial fibrillation or other conditions may participate, provided they are on stable doses of anticoagulant therapy * Febrile illness within 7 days of study enrollment * History of allergic reactions attributed to compounds of similar chemical or biologic composition to TAS-102 or other agents used in this study * Other anticancer or experimental therapy. No other experimental therapies including for other disease indications are allowed while the participant is receiving study treatment * Women who are pregnant or breast-feeding * Participants with any other concurrent medical or psychiatric condition or disease which, in the investigator's judgment, would make them inappropriate candidates for entry into this study * Participants with a history of a prior malignancy within the past 5 years, except for adequately treated basal cell or squamous cell skin cancer or in situ cervical cancer