Although there won't be any hydrogen in the Sun's core, there will be hydrogen just outside the core, and this hydrogen will be able to fuse. This will make the star extremely bright. Moreover, the energy from the fusion shell with produce radiation pressure and literally blow the outside of the Sun outward, making the Sun expand. The Sun will expand so much that it will swallow up the planets Mercury, Venus, and the Earth. The Sun will be a bright red giant star.
All stars become red giants when they run out of hydrogen in the core.
That explains why there is no pattern to the masses of red giant stars.