In the Christmas special "Voyage of the Damned" (Tenth Doctor), The Doctor explains the TARDIS is programmed to lock onto the nearest centre of gravity when it's adrift (in this case, Earth).
That's all great when the nearest centre of gravity is a planet. But what if it's a star or a black hole?
We know from "The Satan Pit" that:
The Time Lords invented black holes.
We also know from several other, older episodes that:
The Time Lords have been known to have a stellar manipulator which can influence the lifespan of a star.
But to the best of my knowledge, we don't know whether the TARDIS is capable of flying right through a star or a black hole. With all other type of spacecraft I'd guess the craft would perish, but the TARDIS is a bit odd.
The TARDIS has a forcefield, but I don't know whether that will hold in the extreme cases of crashing into a star or black hole (let's keep the relativistic effects of "crashing into" a black hole out of it for simplicity's sake).
The real question is of-course whether this safeguard could cause the TARDIS to destroy itself by crashing into a star, black hole or anything similar.
Any episodes confirming or disproving the TARDIS' abilities in this regard are welcome. Canon answers are preferred.