kilobug comments on Harry Potter and the Methods of Rationality discussion thread, February 2015, chapter 109 - Less Wrong Discussion
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My understanding is that "unbreakable" magic makes the object unable to change at macroscopic level, but doesn't prevent small alterations at microscopic level. And those small alterations at microscopic level, in case of a transfigured human, will lead to DNA damage and similar things. It's not known if the information encoded in the brain will resist or not - it's much higher level than DNA, so there is a good chance it would.
Another possibility if that "unbreakable" works fine on things that have very few moving parts, but if you try that on a human body then they become utterly incapable of changing. Their muscles don't flex, which means they can't breathe and their heart stops beating, and they die very quickly.