To resolve the black hole information paradox it has been argued that quantum gravity effects must destroy the classical black hole horizon and replace it by horizon-sized structure. While rather bold, this claim is supported in string theory whose very ingredients - extra dimensions, topology and fluxes - can be used to build such black hole microstates. To establish their relevance for astrophysical black holes one has to explain how they can from in the gravitational collapse of a massive star. In a toy model of gravitational collapse, I will study the possibility that microstate geometries can arise dynamically from quantum tunneling processes and argue, based on explicit tunneling amplitude computations, that these effects may stop the collapse to a black hole.