The process in which locally confined epithelial malignancies progressively evolve to become invasive cancer cells is associated with the acquisition of cell motility, fostered by a tissue-level phase transition (PT) from a solid-like to a liquid-like state, known as unjamming. The biomolecular machinery behind unjamming and its pathophysiological relevance have only begun to be unraveled. Using a combination of physical approaches, ex vivo and in vivo model systems, we will address these issues and discuss whether an endocytic-driven PT between “solid” and “liquid” states of cell collectives is a complementary gateway to cell migration in pathology, focusing specifically on the progression of early breast cancer lesions that become locally invasive. We will show how the dynamic changes associated with PT feature the coexistence of long-range coordinated motion and local cell re-arrangement and are sufficient to promote matrix remodeling, and local invasion and exert mechanical stress on individual cell nuclei. This is accompanied by profound transcriptional rewiring, with the unexpected activation of an inflammatory response, change in cell state, and the emergence of malignant traits. Noticeably, carcinoma is composed of a heterogeneous set of cells that differ not only in their genetic landscape but also in their mechano-phenotypes. The impact of mechano-heterogeneity on tissue-level jamming transition is poorly understood. Here, we will also discuss unpublished findings that suggest that contact percolation, a purely geometrical feature, can impact the collective migratory behavior of tissues and, strikingly, promote the activation of an inflammatory gene transcription program in normal and breast carcinoma models