We investigate the origins for the very large adherence of foam tapes and their peculiar mechanisms of debonding by combining instrumented peeling tests with optical imaging of the debonding region and scanning electron microscopy imaging of the damage mechanisms. The main finding is that the exceptional performance of these foam tapes is driven by the presence of a dense array of microscopic hollow spheres that debond from the soft and dissipative adhesive matrix during peeling. This allows the tape to be very stiff and incompressible during holding conditions, while converting to a soft dissipative and compressible foam under critical solicitations. The loss of constraint due to the development of such a diffused damage by local cavitation around the microspheres is responsible for the development of large dissipative strains through the whole large thickness of these tapes as well as exceptional release of stress concentration.