Testing the Addition of an Anti-Cancer Drug, Camonsertib, to Radiation Therapy for Recurrent Head and Neck Squamous Cell Carcinoma

Inclusion Criteria: * Patients must have histologically confirmed recurrent or metachronous (second primary) unresectable head and neck squamous cell carcinoma involving the oral cavity, oropharynx, larynx, hypopharynx, and/or paranasal sinus, or cervical lymphadenopathy with unknown primary. Core needle biopsy (preferably at least three 18-gauge cores) or incisional biopsy is preferred over fine needle aspiration (FNA) for diagnosis of recurrent disease or new primary head and neck squamous cell carcinoma to provide sufficient tumor tissue for correlative studies. Unresectable refers both to patients who have declined surgery and patients deemed unresectable by otolaryngology. This includes patients for whom curative resection is medically contraindicated and/or would be associated with excessive surgical risk (as deemed by the consulting otolaryngologist) or undue surgical morbidity (e.g., total glossectomy, laryngectomy, and/or major resection requiring free flap reconstruction). There are no requirements related to prior systemic therapies that patients may have received * Patients must have recurrent disease within a previously irradiated area (radiotherapy to dose ≥ 30 gray \[Gy\] and ≤ 80 Gy; in-field recurrence) * Patients must have completed prior radiotherapy at least 6 months prior to enrollment. Due to safety concerns, reirradiation within less than 6 months to the head and neck is very rarely recommended per standard of care * Patients must have measurable disease (at least one measurable lesion) as per Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1. Baseline imaging must include neck CT (preferably contrast-enhanced) and chest CT or skullbase to midthigh PET/CT (preferably with contrast-enhanced neck CT if diagnostic contrast-enhanced neck CT not available). Patients who have undergone surgery aside from biopsy may be included if gross disease is present within the surgical resection bed or at another site * Age ≥ 18 years. Because no dosing or adverse event data are currently available on the use of camonsertib in combination with radiotherapy in patients \< 18 years of age, children are excluded from this study * Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2 (Karnofsky ≥ 60%) * Leukocyte count ≥ 3,000/mcL * Absolute neutrophil count ≥ 1,500/mcL * Platelets ≥ 100,000/mcL * Hemoglobin ≥ 9 g/dL or ≥ 5.6 mmol/L without transfusion or erythropoietin dependency (within 7 days of assessment) * Serum bilirubin ≤ 1.5 × institutional upper limit of normal (ULN) (if total serum bilirubin \> 1.5 × institutional ULN, then direct bilirubin must be \< ULN) * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) ≤ 3 × institutional ULN * Albumin \> 2.5 mg/dL * Glomerular filtration rate (GFR) ≥ 60 mL/min/1.73 m\^2 * GFR can be measured directly or estimated using the site's institutional standards * 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 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 * Ability to take pills by mouth * The effects of camonsertib on the developing human fetus are unknown. For this reason and because ATR inhibitors and radiation are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for 6 months after completion of camonsertib administration. 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 * Patients who are receiving any other investigational agents for a current cancer diagnosis * Patients with distant metastatic disease * Patients who have received more than one prior course of head and neck radiotherapy overlapping the region to be treated with the current diagnosis of head and neck cancer * Patients who have disease surrounding \> 180 degrees of the carotid artery * Patients with tumors invading the mandible or tumors with gross skin involvement (i.e., tumor ulceration through the skin) * History of allergic reactions attributed to compounds of similar chemical or biologic composition to camonsertib or radiation * 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 camonsertib is an ATR inhibitor 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 camonsertib, breastfeeding should be discontinued if the mother is treated with camonsertib. These potential risks may also apply to other agents used in this study * Patients diagnosed with scleroderma * Concomitant use of strong CYP3A4/5 inhibitors and inducers, and strong P-gp and BCRP inhibitors * 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