I think the confusion is in your interpretation of the phrase, "collapse into nothingness." A sufficiently massive neutron star does not stop collapsing when the neutrons get close enough together to see the strong close-range repulsive potential of the neutrons, but just keeps on shrinking to a point; that part is right, but it is wrong to think that because it becomes infinitely small it loses some of its gravitational "oomph". Quite the opposite: in fact, the collapsed object (once called a "collapsar") is just what we mean by a "black hole" -- although of course there are lots of possible complications associated with its spin and electrical charge.
So just remember, a black hole is a collapsed neutron star (or something even heavier). There may be smaller and lighter black holes around too, but they would probably have to be left over from the Big Bang.
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