In the comics, Magneto rips out his skeleton at one point. After which Xavier telepathically lobotomizes him. And yes, although Logan nearly dies, he grows a new skeleton including bone claws. His healing factor also goes into overdrive since it doesn’t have to fight against the toxic adamantium all the time. It makes him grow more feral too, until writers decided it got too stupid with Logan talking and acting like a caveman so he got the adamantium back.