Food web structure plays an important role when determining robustness to cascading secondary extinctions. However, existing food web models do not take into account likely changes in trophic interactions ('rewiring') following species loss. We investigated structural dynamics in 12 empirically documented food webs by simulating primary species loss using three realistic removal criteria, and measured robustness in terms of subsequent secondary extinctions. In our model, novel trophic interactions can be established between predators and food items not previously consumed following the loss of competing predator species. By considering the increase in robustness conferred through rewiring, we identify a new category of species--overlap species--which promote robustness as shown by comparing simulations incorporating structural dynamics to those with static topologies. The fraction of overlap species in a food web is highly correlated with this increase in robustness; whereas species richness and connectance are uncorrelated with increased robustness. Our findings underline the importance of compensatory mechanisms that may buffer ecosystems against environmental change, and highlight the likely role of particular species that are expected to facilitate this buffering.