Abemaciclib in Treating Patients With Surgically Resectable, Chemotherapy Resistant, Triple Negative Breast Cancer

Inclusion Criteria: * Women of age \>=18 years * PRE-REGISTRATION: Clinical T1-4, N0-3, M0 breast cancer at diagnosis (prior to the start of neoadjuvant chemotherapy) by American Joint Committee on Cancer (AJCC) staging version 8. * Note: Benign breast disease, lobular carcinoma in situ (LCIS) or ductal carcinoma in situ (DCIS) in the ipsilateral or contralateral breast is allowed. * Note: Additional ipsilateral or contralateral invasive breast cancer is allowed. The index lesion is the largest triple-negative, chemotherapy-resistant lesion. * PRE-REGISTRATION: Histological confirmation of triple negative invasive breast cancer (defined as estrogen receptor \[ER\] =\< 10%, progesterone receptor \[PR\] =\< 10% and HER2 not amplified by in situ hybridization \[ISH\] or immunohistochemistry \[IHC\] 0/1) at diagnosis. * PRE-REGISTRATION: Cohort A: CLOSED TO PRE-REGISTRATION and REGISTRATION as of protocol amendment 6 (04/14/2023) Neoadjuvant chemotherapy (NAC) with one of the following regimens that was not discontinued early due to intolerability with less than 50% of planned treatment given due to disease progression or patient request: * Paclitaxel or docetaxel followed by one of the following: the combination of doxorubicin and cyclophosphamide (AC); the combination of epirubicin and cyclophosphamide (EC) or the combination of 5-fluorouracil, epirubicin and cyclophosphamide (FEC) * Note: Carboplatin may be added to these regimens * AC or EC or FEC followed by …