That's not accurate. Only the inner core collapses (hence the "core-collapse supernova"; there are also other types), the rest rebounds, is heated up by core-produced neutrinos, and gets ejected. The Wikipedia article is a good start, also there are plenty of good papers on arxiv (e.g. on still-not-too-successful numerical modeling of the aforementioned "heating", without which the thing simply doesn't go bang).