and then the stone gets reduced to slag...
can it regenerate later?
There is no regeneration while it's petrified because being turned to stone does not cause HP damage and therefore cannot be regenerated. He's stuck forever as a chunk of stone.
Reducing the stone to slag means it's still stone, right? Being reduced to slag is not a game term I know of, so I'm assuming the stone was simply melted by heat or magic but it's still stone?
If he's returned to flesh after being reduced to slag, that's probably a fatal amount of damage. But is it "hit point damage"? If it is, he can regenerate it. If not, he can't. Per the description of Regeneration.
If the character's petrified body is incomplete when it returns to flesh, the body is likewise incomplete and there is some amount of permanent hit point loss and/or debilitation.
So this seems to be entirely up to the GM.
If he assigns a "hit point loss", then it can be regenerated. If he assigns a "debilitation", it's likely that it can be regenerated too, but your GM might get clever with his debilitation and phrase it in a way that in cannot be regenerated, at his discretion.
Thanks