In the theory of quantum mechanics, information is never destroyed. However, the other great theory of modern physics is general relativity. Physicists don’t know how to put these theories together. The physicists who are working on this would very much like to answer the question you asked about black holes and information. They call your question the black hole information question. To read about black holes, information, fire walls, etc check out this link:

No, information can almost certainly never be created or destroyed.

There are some theories that black holes destroy information, but a definite consensus has emerged around the theories of quantum information which say a black hole can’t do this. The best way to explain is this.

As an object approaches a black hole, it is slowed by the black-hole’s gravity, which curves space and time around it. From our perspective as an outside observer, the object’s never actually falls into the black hole. Time slows to zero at a point call the event horizon, and we see the object (and its information!) smeared across the surface of the even horizon. So the information is never slowed.

Chris’ link is really good on explaining what might happen to the information when a black hole evaporates. There are different theories, but almost everyone now agrees the information is never lost.

Now, wavefunction collapse is much harder to visualise. The point is this: in order to collapse a wavefunction, it needs to be hit/measured by another particle. That particle increases it’s “information” by means of the interaction, in precisely such a way that information is not actually destroyed. Essentially the particle gains a property called “information entropy” which means its information content increases by means of the interaction.
The mathematics behind this process is ludicrously complicated.

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