Pretend that you could cool everything down and allow it to collapse. It would be a very cold white dwarf star.
The pressure at the core would be powerful enough to cause fusion and restart the star. You would probably end up with mostly carbon with some other elements like oxygen, nitrogen and neon, with an outer layer of hydrogen and helium.
But I am going to ignore that new fusion and just look at the hydrogen and helium.
Hydrogen at high enough pressures will turn into a metal. Helium to the best of our knowledge will always remain a liquid, but it could change into a superfluid (temperature has to be low enough).
But more interesting is that the pressure in the collapsed sun would be sufficient to cause electron degeneracy. This means that the atom structure would collapse under the pressure and the electrons would occupy quantum positions. Kind'a like that old plum pudding model of matter. This is a very dense state of matter. The next step would be the collapse into a neutron star via electron capture.
So, what you would have is a core of electron degenerate hydrogen and helium. This would be a quasi-solid. As you proceed towards the surface you would find a layer of solid metalic hydrogen and liquid helium. As you get closer to the surface the hydrogen would turn to liquid. Once reaching the surface, you would have a small, dense atmosphere
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If you are just interested in what is currently in the sun's core, it is a hot, dense plasma -- which is really an ionized gas, but is so compressed that it is denser than a liquid. (It is compressed, but it is not an electron degenerency state which is much denser)