fainting
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Characters becoming unconscious and collapsing due to (mental) shock, asphyxiation, blood loss, etc.
The medical term is Syncope, which strictly refers to the brain not getting enough blood and temporarily shutting down, recovering in a few second when it gets enough blood.
For danbooru however, fainting refers to merely to the act of becoming limp and collapsing.
Also applies to a character that has fainted, though not to be confused with sleeping.