It's not a stupid question at all, here's the answer:

Electrons (as an example) experience Coulomb pressure (charge repulsion), but also a quantum statistical pressure called Fermi Degeneracy pressure related to their kinetic energy, AND ultimately the Pauli Exclusion Principle (Identical Fermions cannot occupy the same state, but higher momentum states take more energy to reach naturally so this creates resistance to collapse). If you want to learn more about this you can get a lot of mileage out of some reading on Fermi-Dirac statistics, the Pauli Exclusion Principle, and degeneracy pressure. Now this is just using electrons as a model, but ultimately all of the above can be overcome by gravity. When it does you still can't have electrons disobeying the rules, but the potential energy barrier to merge electrons and protons into neutrons is overcome. THEN you have neutron degeneracy pressure, and in theory after that you have a black hole (spacetime singularity surrounded by an event horizon.

However... that may not be the case. It is true that observation has confirmed the existence of objects that are so dense and massive they must have an event horizon, but beyond that we have no way of direct observation, right now (even in principle). A lot of people believe this indicates that a singularity doesn't really exist; it's the usual lesson when a singularity appears in your math: your math is wrong. In the end maybe there's another sort of degeneracy pressure from quarks or something even more fundamental like strings that ultimately prevents final collapse to a true singularity.

ed: typos

Thanks! Lots of information for me to learn about.

I assumed they can occupy the same space due to superposition principle, as waves could stack and modulate each other, sort of like wave A and wave B occupying the same space could produce a wave A+B

So a singular point would be the sum of all waves occupying the space.

But maybe gravity or spacetime itself is a recursive function and black holes are functions without a base case and there is no singular point, only non-terminating recursion.

Some ideas to funnel into AI so I can entertain myself hah

The world is made of two types of particle - fermions and bosons. A difference between them is that fermions can not occupy the same quantum state (the Pauli exclusion principle) while bosons can exist as superpositions. Matter is made of electrons, protons and neutrons which are fermions, while the forces are photons, gluons, W , Z and Higgs which are bosons.

In a black hole though … who knows

There is a difference between "being in a superposition" and "occupying the same space". The uncertainty principle basically tells you that an electron is never in a defined place - it exists with some probability in many different places (technically it could be at a definite position, but only if it had completely indefinite momentum, and that's not physically meaningful given energy constraints).

Now, say we have an experiment where two different sources each fire one electron in some direction; and say the electrons have the same spin and other properties except for their initial position and momentum. We can meaningfully say that for a certain location between the two sources there is some > 0 probability for either electron to be there, so the amplitude of each electron's wavefunction at that position is > 0. However, that doesn't mean we can ever find both electrons at that same postion at the same time: the individual wavefunctions are just parts of the two-electron system's wavefunction, and, per the Pauli exclusion principle, that one will be 0 for any state of the form "electron A at position x and electron B at position x". So, for any position, you can find either electron there, but never both.

An additional wrinkle is that this only applies for two identical electrons. If the electrons have different spins, then they can actually be found at the same location at the same time. You can have a spin-up and a spin-down electron in the same place at the same time, but not two spin-up electrons. This is the fundamental property of fermions. However, you can have any number of identical photons at the same location - that's the fundamental property of bosons.

They can't exactly occupy the same space due to the Pauli exclusion principle. IIRC that's believed to be the final "barrier" that prevents neutron stars from collapsing into black holes. But this is also getting into the tricky parts of wave particle duality, so the precise details are a bit difficult for me too.

Only cats can violate Pauli's principle. Anybody who had a cat can attest to the fact they can go through walls. Just close a room with a cat inside and - given enough time - the cat will escape.

So Schrödinger’s cat has an orthogonal state!

(not inside the box)

Actually, the third possible state is Bloody Furious.

How could you measure that the cat was inside the room?

Thermal residue?

If particles were zero size, they would be already black holes. That's the fix introduced by string theory: particles aren't zero size there.