This paper presents a model to explain the phenomenon of large but rare cascades triggered by small initial shocks in various systems, such as cultural fads, collective actions, and infrastructure failures. The model is based on a sparse, random network of interacting agents where decisions are made based on the actions of neighbors according to a threshold rule. Two regimes are identified: one where cascade propagation is limited by network connectivity, leading to a power-law distribution of cascade sizes, and another where it is limited by node stability, resulting in a bimodal distribution. The most connected nodes are more likely to trigger cascades in the first regime but not in the second. Heterogeneity in thresholds and degree distributions plays an ambiguous role in system stability, with heterogeneous thresholds increasing vulnerability and heterogeneous degree distributions reducing it. The paper also discusses the implications of these findings for understanding the robust yet fragile nature of complex systems.This paper presents a model to explain the phenomenon of large but rare cascades triggered by small initial shocks in various systems, such as cultural fads, collective actions, and infrastructure failures. The model is based on a sparse, random network of interacting agents where decisions are made based on the actions of neighbors according to a threshold rule. Two regimes are identified: one where cascade propagation is limited by network connectivity, leading to a power-law distribution of cascade sizes, and another where it is limited by node stability, resulting in a bimodal distribution. The most connected nodes are more likely to trigger cascades in the first regime but not in the second. Heterogeneity in thresholds and degree distributions plays an ambiguous role in system stability, with heterogeneous thresholds increasing vulnerability and heterogeneous degree distributions reducing it. The paper also discusses the implications of these findings for understanding the robust yet fragile nature of complex systems.