That's actually an interesting question I never really gave this much thought before 🤔

There's a high chance I may be wrong but I think to answer this we'd have to consider what makes a wizard, well, a wizard. If it's the fact that they have powers and powers alone then they should indeed die like a human when they lose them.

However, if it's due to the fact that they are biologically born to be closer to spirits and magical creatures more than humans no matter then they should (theoretically) still shatter all the same. (At least I think they should...?)

(If there was a way to see if any creatures that may be mythical or of the magical type but hold no inherent magic powers themselves turn to stone when they die then perhaps the same could be said for the wizards but I don't think there's been any instances of that so far?)

(I also feel like it would kind of be an easy way out for anyone that would rather not turn to stone to just break a promise near the end of their life and then have a body to leave behind. So maybe it just may not be possible story wise too?)