It becomes a black hole, but it doesn't necessarily collapse, at least not at first. A supermassive black hole has very low density and a very gentle gravitational gradient.
All of the mass does end up in the singularity, in finite time (at least for any finite subset of the black hole), but it doesn't automatically become super dense just because it's a black hole. It can remain quite ordinary for a very long time.
In the formula for a Schwarzchild black hole, the mass is proportional to the radius. Since volume goes up with the cube of the radius, the density drops quickly.
The kind of black hole that forms from a collapsing star is super dense. But a supermassive black hole forms differently, as a denser region of gas and stars during galaxy formation. The density can be lower than that of water. You could be inside it without even realizing anything is odd.
There is no known way to form black holes bigger than that. We had been discussing a pure thought exercise. Though it is possible that the universe as a whole has enough density to be a black hole. (Signs point to no, but it's an open question.)
Wait, can you take this a little slower? I was not aware black holes could have sensible density.