Better yet, the sun cannot run out of fuel, but it can get sufficiently contaminated with higher elements to change its nature. Also the process is likely far slower than we ever imagined. Even surplus gravity is been carried away to prevent excessive build up. We do not need a black hole to do this. I suspect that as a Star matures, its reaches a point that it needs to shed its impurities and then may even lose enough of the gravitational field to literally blow apart. We have to see this actually happen though.