Background/Objectives: The tumor microenvironment (TME) plays a crucial role in the progression of the malignant phenotype through several mechanisms, such as hypoxia and nutrient deprivation, among others. These insults activate several intracellular pathways, and among them are ER stress and the unfolded protein response (UPR). Our aim was to assess if a specific ER stress inducer causes an exacerbation of the malignant phenotype of anaplastic thyroid carcinoma (ATC) cells. Methods: We used an ATC cell line, FRO cells, that had not undergone a full Epithelial–Mesenchymal Transition (EMT) and an ER stress-adapted cell line derived from FRO cells, A400 cells. Western blot, immunofluorescence, scratch, and invasion assays were used to evaluate the response of the FRO and A400 cells to ER stress. Results: The FRO cells were subjected to high-level ER stress caused by 400 ng/mL of tunicamycin (Tn). This caused the death of a large fraction of cells, but eventually a population emerged that we called A400 cells. Following an over challenge with Tn, the adapted population showed suppression of the UPR, apoptosis, and stress kinase activation. Moreover, the adapted population showed an exacerbation of mesenchymal features with a more invasive phenotype. At the level of a single cell, the adapted cells, caught in the act of moving, showed high-level expressions of vimentin (VIM), fibronectin (FN), and N-cadherin. Conclusions: High-level ER stress acts as a selection factor favoring the emergence of a cell population showing “mesenchymal drift” with a more malignant phenotype.