In a core-collapse supernova, after the explosion is launched, neutrino heating above the protoneutron star creates an outflow of matter. This outflow has been extensively investigated as a nucleosynthesis site. Here, we revisit this problem motivated by the modeling of neutrino flavor transformations. In this case, it is crucial to understand whether the outflow has a termination shock: its existence observably alters neutrino oscillations a few seconds into the explosion. We derive physical criteria for the formation of this shock, in terms of neutrino luminosity, average energy, protoneutron star radius and mass, and the postshock density. For realistic physical conditions, the system is found to be on the edge of shock formation, thus reconciling seemingly disparate numerical results in the literature. Our findings imply that neutrino signatures of modulated matter effects are a sensitive probe of the inner workings of the supernova.
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