Any clump of mass smaller than its own Schwarzchild radius will have an event horizon, but that doesn't necessarily mean that all that mass needs to wind up as a point. Under what we currently think we know about gravity a clump compressed to that radius will wind up as a singularity, but it's possible that we might have something wrong about gravity which would result in black holes with event horizons but no singularities -- instead you'd just have some high-but-not-infinite density mass in the middle being prevented from collapsing by... something we currently don't understand.