So when it comes to true vacuum Quantum Field Theory proves that things are not as simple as they appear on our human macro level. Basically, there is no such thing as true vacuum in an absolute sense.
As far as things moving towards a vacuum, it is just stuff taking the path of least resistance at a simple level. Think of air and gases just like a slightly different liquid compared to water. Air and water flow in a very similar way. If you displace water by making a boat, the displaced water is always looking to get back into the displaced space. A vacuum is a similar displacement void that is fighting against everything else that wants to occupy that space.
Honestly, I’ve come across many things where I asked questions like this. I could be wrong, but it is likely that you are thinking of vacuum as some kind of state or force. It is not. Vacuum is the lack of baryonic matter. Maybe you have encountered this one before: “cold does not exist.” Cold is always a relevant thing and really it is a human invention to relate ideas. Nothing can be at true absolute zero in the universe as the motion of atoms is tied to time and entropy. So cold is always just the absence of heat or really, the absence of energy. Much the same, a vacuum is the absence of matter. The main thing that might move matter into a region of vacuum is gravity, or to a much lesser extent possibly magnetism depending on the properties of a gas.
As far as black holes, no vacuum can exist in a black hole. Once matter gets past the event horizon humans do not know any testable physics. Technically, as it is currently explained there is a singularity somewhere inside the event horizon. This singularity is the merging of both space and time. The merging is because you are being pulled at light speed the moment you pass the event horizon. You’re moving at the speed of time which makes physics break. Moving at the speed of time, means you are already merged with the singularity the moment you pass the event horizon, however the event horizon is larger than the singularity itself. The singularity, as we understand it, is time as much as it is space, literally “spacetime.” If it could be seen, theoretically, we could also see all of time on its surface…if it could be called a “surface.” A black hole is not really an object as much as it is a state.