I am not sure what you mean by a black hole collapsing. A black hole solution in general relativity is a vacuum solution - there is nothing to actually collapse. The additional fields and particles are are uasually thought of as test particles, meaning that they don't contribute to the geometry/gravity.
Test particles will hit the singularity - at least classically.
Not for test particles - if you had enough mass inside the horizon then it may not be a black hole solution. For example, the Schwarzschild works fine for the external space-time of say the Sun. There is no horizon here as it would sit inside the Sun, but in that region we do not have a vacuum solution, thus we need some other solution to the field equations - so called interior solutions..
Usually we treat them as only being acted on by gravity and not creating any gravity. But this is an approximantion that is thought to be okay.