Testing the Addition of a Radiation Sensitizing Drug, IPdR, to the Usual Chemotherapy Treatment (Capecitabine) During Radiation Therapy for Rectal Cancer

Inclusion Criteria: * At diagnosis, patients must have had histologically proven adenocarcinoma of the rectum with no evidence of distant metastases * At diagnosis, the major portion of the tumor must have been intact, and the following must be documented: * Distance of the lowest tumor margin from the anal verge; and * Intent for sphincter sparing or non-sphincter sparing surgical resection according to the primary surgeon; and * The majority of the untreated tumor must be \< 12 cm from the anal verge or below the peritoneal reflection as determined by the treating surgeon * At diagnosis, the tumor must have been locally advanced stage II (T3-4 N0) or stage III (N positive \[+\]) rectal cancer with at least one of the following: * Distal location (as defined by measurement on magnetic resonance imaging \[MRI\], endorectal ultrasound \[ERUS\]/pelvic computed tomography \[CT\] \[with intravenous (IV) contrast\] scan or palpable on digital rectal exam \[DRE\]): cT3-4 =\< 5 cm from the anal verge, any N * Bulky: Any cT4 or evidence that the tumor is adjacent to (defined as within 3 mm of) the mesorectal fascia on MRI or ERUS/pelvic CT (with IV contrast) scan * High risk for metastatic disease with 4 or more regional lymph nodes (cN2). Clinical Nodal or "cN" status for eligibility includes the total number of nodes (N2 = 4 or more) in the mesorectal and superior rectal stations measuring \>= 1.0 cm in any axis on cross sectional or endoscopic imaging. Nodes must measure 1.0 cm or greater to be considered positive for this eligibility requirement * Not a candidate for sphincter-sparing surgical resection prior to neoadjuvant therapy (as planned by the primary surgeon) * Patients must have received 8 cycles of neoadjuvant leucovorin, fluorouracil, and oxaliplatin (mFOLFOX) and must have completed this therapy at least 3 weeks (and no more than 6 weeks) prior to enrollment on this study * Patients must intend to undergo surgical resection of the rectal primary tumor following chemoradiotherapy * Age \>= 18 years * Because no dosing or adverse event (AE) data are currently available on the use of IPdR in combination with capecitabine and RT in patients \< 18 years of age, children are excluded from this study, but will be eligible for future pediatric trials * Eastern Cooperative Oncology Group performance status =\< 2 (Karnofsky \>= 60%) * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,200/mcL * Platelets \>= 100,000/mcL * Hemoglobin \> 10 g/dL * Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) =\< 2.5 x institutional ULN * Alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional ULN * Creatinine =\< 1.5 x institutional ULN OR glomerular filtration rate (GFR) \>= 60 mL/min/1.73 m\^2 * Alkaline phosphatase =\< 3 x institutional ULN * Sodium, potassium, chloride, bicarbonate, and magnesium within institutional normal limits * Patients with acquired immunodeficiency syndrome (acquired immunodeficiency syndrome \[AIDS\]-related illnesses) or known human immunodeficiency virus (HIV) disease must: * Have a CD4 count \>= 200 cells/uL within 30 days before enrollment, * Be off all antiretroviral therapy (prophylaxis/treatment) more than 60 days before enrollment, and * Have no evidence of opportunistic infections * Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured and be receiving no therapy * 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 2B or better * Patients must have the ability to swallow and retain oral medication * The effects of IPdR on the developing human fetus are unknown. For this reason and because radiosensitizing agents as well as other therapeutic agents used in this trial are known to be teratogenic, women of child-bearing potential (WOCBP)\* and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. WOCBP must have a negative urine or serum pregnancy test within 72 hours prior to enrollment. If urine pregnancy results are positive or cannot be confirmed as negative, a serum pregnancy test will be required. 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. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of IPdR administration * Women of childbearing potential (WOCBP) is defined as any female who has experienced menarche and who has not undergone surgical sterilization (hysterectomy or bilateral oophorectomy) or who is not postmenopausal. Menopause is defined clinically as 12 months of amenorrhea in a woman over 45 in the absence of other biological or physiological causes * Ability to understand and the willingness to sign a written informed consent document. Participants with impaired decision-making capacity (IDMC) who have a legally-authorized representative (LAR) and/or family member available will also be eligible Exclusion Criteria: * Patients who have not recovered from adverse events due to prior mFOLFOX6 chemotherapy (i.e., have residual toxicities \> grade 1) with the exception of alopecia * Patients who are receiving any other investigational agents * Patients with impaired gastrointestinal (GI) function or GI disease that may significantly alter the absorption of oral IPdR and capecitabine (e.g. ulcerative disease, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome, or small bowel resection). Patients with active inflammatory bowel disease (i.e., patients requiring current medical interventions or who are symptomatic) or have a history of abdominal surgery or other medical condition that may, in the opinion of the treating physician, interfere with GI motility or absorption. Patients with colostomies are allowed unless colostomy is for one of the precluded reasons above * Treatment with warfarin is not allowed. However, therapy with heparin, low molecular weight heparin (LMWH), and DOACs (direct oral anticoagulating agent) such as dabigatran (Pradaxa), rivaroxaban, and apixaban (Eliquis) is allowed * Patients with an active concurrent invasive malignancy * History of prior invasive rectal malignancy, regardless of disease-free interval * Patients who have received pelvic RT for rectal cancer, or prior pelvic RT for any other malignancy that would prevent the patient from receiving the required RT for this study * History of allergic reactions attributed to compounds of similar chemical or biologic composition to IPdR or capecitabine * Patients with uncontrolled intercurrent illness * Patients with psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study because IPdR may have 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 IPdR, breastfeeding should be discontinued if the mother is treated with IPdR. These potential risks may also apply to other agents used in this study * Patients that received live vaccines within 30 days prior to the first dose of trial treatment and while participating in the trial. Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster, yellow fever, rabies, bacillus Calmette-Guerin (BCG), and typhoid vaccine. Seasonal flu vaccines that do not contain live virus are permitted * Known homozygous DPD (dihydro pyrimidine dehydrogenase) deficiency * History of, or any evidence of, active non-infectious pneumonitis * Active autoimmune disease that has required systemic treatment within the past 2 years (i.e., with use of modifying agents, corticosteroids, or immunosuppressive drugs). Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment * History of active TB (Bacillus tuberculosis) * Active or chronic infection requiring systemic therapy * Diagnosis of immunodeficiency or receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of study therapy. The use of physiologic doses of corticosteroids may be approved after consultation with the study principal investigator (PI) * Active seizure disorder uncontrolled by medication * Synchronous colon cancer * Other invasive malignancy within 5 years. Exceptions are colonic polyps, non-melanoma skin cancer, or carcinoma-in-situ of the cervix * Antineoplastic therapy (e.g., chemotherapy or targeted therapy) for other invasive malignancy within 5 years (for the purposes of this study hormonal therapy is not considered chemotherapy)