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

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 chemothe…