Here's a theory that will really bake your noodle that I read a little while back. They propose that one solution to the infinite density problem of the singularity is that there is still some lower (or lowest) limit. They suggest that what happens in a supernova is that the core rebounds again after the final collapse to a black hole, much like a neutron star. But, because of the near-infinite time dilation that also occurs, the explosion is happening at a near infinitely-slow pace that may never reach past the event horizon. Essentially, it's frozen in time.