Our sun isn’t big enough to go nova. It will just slowly die out.
That said, he’s going to be much less dense than the stellar core material, and should float to the surface eventually. Not that it’s going to do much good because there’s still nowhere worth going that’s only a mile from the sun. Best bet would be to keep a sharp eye out for a comet or something (and good luck seeing anything on the surface of the sun) and trying to catch a ride.
Traveling forever though the emptiness of space is only a marginal improvement over being stuck in the center of the sun though.
