Assuming they exist (which seems likely according to our current best theories) black holes are very strange things indeed. In particular, the fate of something heading over the black hole horizon depends seems to be different depending on whether you cross the horizon or not.

In the frame of reference of somebody passing through the horizon, the horizon doesn't seem very special at all - you could cross the horizon of a sufficiently large black hole without even noticing. After passing the horizon, however, escape is impossible and you would inevitably end up spaghettified by the massive tidal forces near the central singularity.

In a frame of reference of somebody outside the black hole, the picture is very different. From that perspective, the gravitational time dilation at the horizon means that the progress of the falling object becomes slower and slower, grinding to a complete stop at the horizon itself. The red-shifting of any photons emitted from close to the horizon also means that the object looks redder and redder, going through infra-red, terahertz radiation, microwaves, and radio waves of increasing wavelength until they are too low energy to detect but they never quite stop altogether.

In the meantime, the black hole evaporates by the process of Hawking Radiation. This takes an unimaginably long time - as long as 10^{100} years for the largest black holes but if you wait there long enough it will happen. Supposing that you could somehow detect the infalling observer during the entire period of the evaporation, you'd see the infalling observer crossing the horizon at the exact moment that the black hole disappeared altogether in a bright flash of energy (the smaller the black hole, the more it radiates). But of course, at that moment the infalling observer has zero mass-energy (as does the black hole as a whole) so how can it be the same observer in its own frame of reference (when its mass is the same as it was before the experiment began)?

Clearly our current theories of physics are insufficient here - we don't yet have a consistent theory of quantum gravity so we just don't know what happens near a tiny black hole when the spacetime curvature is high enough to be in the quantum regime.

One way out of the apparent paradox is simply that the two observers can never compare notes because whatever information the infalling observer collects is inevitably destroyed at the singularity, and no information from inside the black hole can ever be transmitted to the outside universe. The interior of the black hole is causally disconnected from the outside - it can be considered to exist infinitely far in the future (long after the black hole evaporates) or can even be considered to be an entirely different universe in its own right. If the two observers can never get back together to compare notes (and find that they disagree) there isn't really any disagreement. It's a bit like the Many Worlds Interpration of quantum mechanics - observers in different parallel universes can't subsequently interact so they can't disagree about the observable outcome of some experiment.

But in both of these cases there is a philosophical problem - if the universe is qualitatively different for different observers then it seems to make a mockery of the very idea of an objective reality. Just as the IO Monad theory of subjective experience has no problems with observers disagreeing on matters that make no difference in an objective sense, it seems like general relativity may require that we have no problems with disagreements between causally disconnected objective realities.