A spatial avalanche model is introduced, in which avalanches increase stability in the regions where they occur. Instability is driven globally by a driving process that contains shocks. The system is typically subcritical, but the shocks occasionally lift it into a near- or supercritical state from which it rapidly retreats due to large avalanches. These shocks leave behind a signature—a distinct power-law crossover in the avalanche size distribution. The model is inspired by landslide field data, but the principles may be applied to any system that experiences stabilizing failures, possesses a critical point, and is subject to an ongoing process of destabilization that includes occasional dramatic destabilizing events.