Triple-negative breast cancer (TNBC) is a subtype of breast cancer characterized by the absence of estrogen and progesterone receptors (ER, PR) and lacking an overexpression of human epidermal growth factor receptor 2 (HER2). Apart from this lack of therapeutic targets, TNBC also shows an increased capacity for early metastasis and therapy resistance. Currently, many TNBC patients receive neoadjuvant chemotherapy (NACT) upon detection of the disease. With TNBC likely being driven at least in part by a cancer stem-like cell type, we wanted to evaluate the response of primary cancer stem cells (CSCs) to standard chemotherapeutics. Therefore, we set up a survival model using primary CSCs to mimic tumor cells in patients under chemotherapy. Breast cancer stem cells (BCSCs) were exposed to chemotherapeutics with a sublethal dose for six days. Surviving cells were allowed to recover in culture medium without chemotherapeutics. Surviving and recovered cells were examined in regard to proliferation, migratory capacity, sphere forming capacity, epithelial–mesenchymal transition (EMT) factor expression at the mRNA level, and cancer-related microRNA (miRNA) profile. Our results indicate that chemotherapeutic stress enhanced sphere forming capacity of BCSCs, and changed cell morphology and EMT-related gene expression at the mRNA level, whereas the migratory capacity was unaffected. Six miRNAs were identified as potential regulators in this process.