What exists between a black hole's event horizon and its singularity?
We can't be sure what exists between the event horizon and singularity of a black hole.
Our current knowledge of the laws of physics can't describe what goes on inside of a black hole.
Anything which falls inside the vent horizon, by definition, can't escape, not even light. This causes a problem known as the information paradox. If an object falls through the event horizon information about it is lost. This is not allowed.
To get around the information paradox, new physics is required. Stephen Hawking is working on a theory that the information about the object gets stored in the event horizon itself.
General Relativity predicts a singularity inside a black hole. This is a point of infinite curvature of space time and infinite density. Infinities are a problem in both mathematics and physics. New physics is required which may be able to eliminate the infinities.
As we can never see inside a black hole, as far as we know, it is impossible to determine what is inside it. Anything which passes the event horizon must ultimately join the singularity.
Our best theories are that between the event horizon and the singularity are objects which have passed through the event horizon and are heading towards the singularity.