The progression and malignancy of many tumors are associated with increased tissue stiffness. Conversely, the oncogenically transformed cells can be confined in soft stroma. Yet, the underlying mechanisms by which soft matrix confines tumorigenesis and metastasis remain elusive. Here, we show that pancreatic cancer cells are suppressed in the soft extracellular matrix, which is associated with YAP1 degradation through autophagic-lysosomal pathway rather than Hippo signal mediated proteasome pathway. In the soft stroma, PTEN is upregulated and activated, which consequently promotes lysosomal biogenesis, leading to the activation of cysteine-cathepsins for YAP1 degradation. In vitro, purified cathepsin L can directly digest YAP1 under acidic conditions. Lysosomal stress, either caused by chloroquine or overexpression of cystatin A/B, results in YAP1 accumulation and malignant transformation. Likewise, liver fibrosis induced stiffness can promote malignant potential in mice. Clinical data show that down-regulation of lysosomal biogenesis is associated with pancreatic fibrosis and stiffness, YAP1 accumulation, and poor prognosis in PDAC patients. Together, our findings suggest that soft stroma triggers lysosomal flux-mediated YAP1 degradation and induces cancer cell dormancy.