Soft adhesive pads attached to a rigid substrate show stick-slip behavior upon loading: they detach and reattach in a different location. This is accompanied by the lifting of the adhesive, the mechanical wave carrying this motion being known as a Schallamach wave. Especially for pads with a stiffer backing that are loaded parallel to the substrate, the reattachment behavior is crucial for the determination of the failure mechanism. Here we use finite element simulations to capture this kind of behavior, making use of tailored reversible cohesive elements allowing this type of reattachment. We manage to reproduce and explain the driving force for the behavior. While the observation of this type of Schallamach waves is widely recognized, and while numerical methods have been developed to deal with adhesion-friction coupling in adhesive spheres or cylinders, their representation past the instance of reattachment in finite element simulations of soft adhesive surface-surface interactions is new. We suggest that with rather limited and straightforward interventions in the cohesive law, reattachment can now be represented for soft adhesive detachment, but also in other fields. The better understanding of the mechanics driving this type of behavior and the different detachment modes, could inspire further applications in robotic grippers and even in earthquake engineering.