Enhanced coalescence in driven foams

External driving leads to the emergence of unique phenomena and properties in soft matter systems. We show that driving quasi-2D foams by mechanical vibration results in significant bubble coalescence, which is enhanced in the presence of a continuous phase with a solid-like rheology, here provided by a concentrated emulsion. The interplay between coarsening and coalescence can be modulated through vibration amplitude and foam liquid fraction, which can be used to create unusual structural motifs. The late-stage dynamics suggest an analogy with fracture-type viscoelastic phase separation, in which rupture and slow structural relaxation play a central role. The combined effect of coarsening and coalescence is captured through a statistical model that quantitatively describes the time evolution of the number of bubbles.