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In my world, roughly equivalent to present day earth, a secret experimentation program has succeeded in creating a genetically engineered super-soldier, more by accident than skill. No magic or anything - just pure dumb experimental luck (after many, many failures. These people have no morals). Of course, their success means their imminent destruction, as this guy they created doesn't like being experimented on, and they have no way to control him, but that's beside the point :)
One of the genetic enhancements this guy has is rapid healing. Similar to wolverine of the X-Men, except that in this case the healing works in every way the same as a normal human healing, only at a much more rapid pace - even the worst injuries heal in a matter of minutes. That, of course, has some negative side effects - for example, if a broken bone isn't set immediately (no adimantium in this world, so bones will break just as easily as ever), it will heal crooked, just as if a broken bone wasn't set in a normal person - only way faster. A lost limb wouldn't grow back, but the stump would heal over before he could bleed to death from it.
One thing I'm not sure of though is what sort of toll such healing would take on the body? Presumably healing uses resources from the body - I would assume, for example, that healing a bone would use calcium and other minerals. Normally such healing is spread out over a long enough time that said resources could be replenished by normal consumption, but in his case it all happens at once, which presumably could drain the body of needed resources.
Is there some level of injury at which the body wouldn't have enough resources to complete the healing? What would happen then? For more minor injuries, how much, if any, effect would the rapid healing of those injuries have, for example leaving him tired or hungry? Would it be possible for him to die of an otherwise non-fatal wound because of the rapid healing "draining" him too much, such that organs start shutting down?
Edit: Lets say that he was in the lab for a while being experimented on before breaking out and destroying it, during which time the scientists were running experiments to test his limits. As such, he would learn from them what effects to expect, and what he would need to do to deal with them (since obviously the scientists don't want him to die, since he is their first success and they don't really know why he worked). How would that knowledge gleaned from the tests change things?