| FractalLaw |
Fast healing is not regeneration. If an undead is dropped to 0 or less HP then it is destroyed, ending fast healing. It does not come back.
If you're talking about a bloody skeleton, then that does not come back to life due to the fast healing ability but rather their deathless ability. Their fast healing only resumes when they come back due to deathless.
I'm not aware of any specific rules that cover this, but it's still the same skeleton, so I'd say your player would still have control.