Testing the Addition of an Anti-cancer Drug, Berzosertib, to the Usual Treatment (Radiation Therapy) for Chemotherapy-Resistant Triple-Negative and Estrogen and/or Progesterone Receptor Positive, HER2 Negative Breast Cancer

This phase Ib trial studies the best dose of berzosertib when given together with the usual treatment (radiation therapy) in treating patients with triple negative or estrogen receptor and/or progesterone receptor positive, HER-2 negative breast cancer. Berzosertib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Radiation therapy uses high energy rays to kill tumor cells and shrink tumors. Giving M6620 and radiation therapy may kill tumor cells more effectively than radiation alone or shrink or stabilize breast cancer for longer than radiation therapy alone.

PRIMARY OBJECTIVE:

I. To determine the recommended phase 2 dose of twice weekly berzosertib administered concurrently with conventionally fractionated radiation therapy (RT) to the breast/chest wall and regional nodes.

SECONDARY OBJECTIVES:

I. To describe the nature of toxicity that develops when an ATR inhibitor is administered concurrently with RT for breast cancer using provider assessments.

II. To assess long-term locoregional control, disease-free survival, distant disease-free survival, and overall survival of patients treated with this approach.

III. To explore symptomatic adverse events and tolerability of berzosertib being administered concurrently with RT using patient-reported outcomes (PROs).

IV. To assess for alterations in deoxyribonucleic acid (DNA) damage response and repair genes, including effectors and regulators of homologous recombination (HR), in pre-chemotherapy biopsy specimens and post-chemotherapy surgical resection specimens using whole exome sequencing (WES) and ribonucleic acid (RNA) sequencing (RNAseq), and to correlate HR deficiency with disease-free survival.

V. To identify somatic alterations in circulating cell-free DNA (cfDNA) at baseline, mid-treatment, end-of-treatment, and follow-up and to correlate cfDNA with disease-free survival.

EXPLORATORY OBJECTIVES:

I. To compare the baseline and post-treatment skin microbiome and make exploratory correlations with severe provider and patient-reported toxicity.

II. To explore dose-volume parameters associated with acute and late provider and patient-reported toxicity following berzosertib administration concurrent with RT.

III. To identify circulating tumor cell (CTC) positivity at baseline, mid-treatment, end-of-treatment, and follow-up and to correlate CTC positivity or the combination of CTC positivity and cfDNA with disease-free survival.

IV. To evaluate pre-treatment and post-treatment differential abundance of peripheral blood immune cell populations identified by cytometry by time-of flight (CyTOF).

V. To evaluate associations of the pre-treatment and post-treatment peripheral blood immune phenotype (as assessed by CyTOF) with disease-free survival, distant disease-free survival and overall survival.

VI. To explore the USP21-ATR pathway and its association with epithelial to mesenchymal transition (EMT) in therapeutically resistant breast cancer specimens at pre-treatment and post-treatment timepoints using immunohistochemistry (IHC) and RNAseq.

OUTLINE: This is a dose-escalation study of berzosertib.

Patients receive berzosertib intravenously (IV) over 60 minutes twice weekly (BIW) for 5 weeks in the absence of disease progression or unacceptable toxicity. Patients undergo RT 5 days a week for 5-6 weeks depending on the type of surgery undergone. Patients also undergo a collection of blood on study.

After completion of study treatment, patients are followed up weekly for 4 weeks, at 12 months, then yearly for up to 3 years.

Eligibility Criteria:
Inclusion Criteria:

* Males or females age \>= 18 years. Note: Because no dosing or adverse event data are currently available on the use of berzosertib in combination with radiation therapy in patients \< 18 years of age, children are excluded from this study, but will be eligible for future pediatric trials
* Patient with non-metastatic, histologically confirmed primary estrogen receptor (ER) =\< 10%, progesterone receptor (PR) =\< 10%, and HER2-negative breast cancer (triple negative breast cancer \[TNBC\]) either using the baseline biopsy specimen or the post-neoadjuvant chemotherapy (NAC) residual surgical specimen and RCB2 or RCB3, as defined by Symmans et al., 2007, and received neoadjuvant anthracycline and/or taxane-based chemotherapy OR Patient has non-metastatic, histologically confirmed primary ER \> 10% and/or PR \> 10%, HER2-negative breast cancer with RCB3 and received neoadjuvant anthracycline and/or taxane-based chemotherapy OR Patient has locoregionally recurrent TNBC or ER \>10% and/or PR \>10%, HER2-negative breast cancer.

  * Note: Results from any Clinical Laboratory Improvement Act (CLIA)-certified lab are acceptable for the purpose of determining study eligibility.
  * Note: For patients with primary breast cancer, there is no minimum number of neoadjuvant cycles required provided the patient received an anthracycline or taxane preoperatively. Patients with locoregionally recurrent breast cancer are not required to have received preoperative chemotherapy
* Patient has undergone total mastectomy or wide local excision with axillary staging, and the margins of the resected wide local excision or mastectomy specimens are free of invasive tumor and ductal carcinoma in situ (DCIS) or patient has undergone axillary surgery for regionally recurrent breast cancer. Unresected axillary level III, internal mammary, and supraclavicular nodal disease is permitted.

  * Note: For patients who have undergone mastectomy, immediate reconstruction is allowed
* Patients must have completed their final breast surgery, including re-excision of margins for invasive cancer and DCIS, within 90 but not fewer than 21 days prior to registration unless patient received postoperative chemotherapy in which case patients must have completed their adjuvant chemotherapy within 90 days but not fewer than 28 days prior to registration
* The patient must have recovered from surgery with the incision completely healed and no signs of infection prior to registration
* Patients must be proceeding with breast/chest wall and regional nodal irradiation including internal mammary node treatment. For patients with bilateral breast cancer, RT must be indicated and administered only to one side
* Eastern Cooperative Oncology Group (ECOG) performance status =\< 2
* Willing to provide tissue and blood samples for correlative research
* Leukocytes \>= institutional lower limit of normal (LLN)
* Absolute neutrophil count \>= institutional LLN
* Platelets \>= institutional LLN
* Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN)
* Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 x institutional ULN
* Creatinine =\< 1.1 mg/dL OR
* Glomerular filtration rate (GFR) \>= 45 mL/min/1.73 m\^2 for patients with creatinine levels above 1.1 mg/dL
* 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
* Negative urine or serum pregnancy test for individuals of childbearing potential. Note: The effects of berzosertib on the developing human fetus are unknown. For this reason and because DNA-damage repair inhibitors as well as radiation used in this trial 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 and for the duration of study participation, and for 6 months after completion of berzosertib 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. 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 6 months after completion of berzosertib administration
* Ability to understand and the willingness to sign a written informed consent document

Exclusion Criteria:

* Patients who have had chemotherapy within 4 weeks prior to entering the study
* Prior RT to the ipsilateral chest wall or ipsilateral breast or thorax. Individuals with prior RT to the contralateral breast or chest wall are eligible
* 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 and grade 1-2 taxane-induced neuropathy which will be permitted
* Patients who are receiving any other investigational agents or concomitant anti-neoplastic treatment, except endocrine therapies and bisphosphonates which are permitted without restriction even during protocol treatment. Postoperative chemotherapy is allowed but must be discontinued \>28 days prior to registration
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to berzosertib
* Berzosertib is primarily metabolized by CYP3A4; therefore, concomitant administration with strong inhibitors of CYP3A4 (e.g., ketoconazole, itraconazole, clarithromycin, ritonavir, indinavir, nelfinavir, and saquinavir) or inducers of CYP3A4 (e.g., rifampin, phenytoin, carbamazepine, phenobarbital, St. John's wort) should be avoided. Patients requiring any medications or substances that are strong inhibitors or inducers of CYP3A during the course of the study and for 14 days prior to enrollment are ineligible. 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. This includes but is not limited to, ongoing uncontrolled serious infection requiring IV antibiotics at the time of registration, symptomatic congestive heart failure, unstable angina pectoris, symptomatic/uncontrolled cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements.
* Active systemic lupus, scleroderma, or dermatomyositis with a CPK level above normal
* Pregnant women are excluded from this study because berzosertib as a DNA damage repair inhibitor may have the potential for teratogenic or abortifacient. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with berzosertib, breastfeeding should be discontinued if the mother is treated with berzosertib
* Patients with known hereditary syndromes predisposing to radiosensitivity such as Li Fraumeni syndrome and ataxia telangiectasia are excluded from the study. Patients with mutations in breast cancer predisposition genes such as BRCA1, BRCA2, PALB2, CHEK2, and ATM are eligible
* Patients with a prior or concurrent malignancy, excluding non-melanoma skin cancers and non-invasive cancers whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen