First, you've gotta toss the point source model for gravity that works best outside gravitic objects - a=µm/r² kinda breaks down at the center of an object where it tries to divide by zero and predicts an insane acceleration right next to the center, while a quick check with first principles will allow you to realise that gravitic acceleration at the center is actually zero because you're surrounded by equal mass at equal distances in all directions so it all cancels out.

See this stackexchange answer for a neat graph of Earth's gravity gradient vs depth

When a large star goes supernova, the explosion sheds the outer layers but compresses the core, which increases the core section's density at and below the boundary layer - which also serves to increase the gravity since you have the same core mass with a much smaller radius.

If that new stronger amount of gravity is sufficient to continue collapsing the core, you get a runaway effect that ends up with a neutron star or black hole.

Smaller stars can't hit those runaway thresholds, and just leaves white or brown dwarves behind (see Chandrasekhar limit) - but if the escape velocity reaches the speed of light, a black hole will pop into existence where the hyper-compressed core once was, containing all its mass, angular momentum, and charge.