The dynamics of droplets exhibiting an elastic interface generated by a percolated network of particle aggregates at the interface is microscopically investigated in a counter rotating shear flow device. The droplet deformation is significantly suppressed by interfacially localized nanoparticles, even at high Ca numbers, resulting in suspension-like behavior at high particle coverage. When the Ca number surpasses a critical value, the particle network locally breaks up, resulting in localized deformability of the interface and breakup dynamics characterized by extremely irregular shapes. Finally, the destruction of the interfacial network results in hysteresis effects in the droplet deformation