This is a well-understood problem in GR. To an outside observer, things never appear to cross the Schwarzschild radius (R_S), giving the impression that time stops for in-falling matter when it gets to R_S. This, however, is an illusion forced on a distant observer.

The stuff that is actually falling into the black hole never notices R_S because the velocity they measure is not greater than c, and crossing the event horizon is a completely benign event. It's the later extreme tidal forces / spaghettification that destroys in-falling matter.

So it is fair to say that stuff enters a black hole.