It would allow those of us not willing or wanting to kill a particular target to use forms of non-lethal damage (hand-to-hand, blunt weapons/tools such as a blackjack) to incapacitate them by reducing this bar to 0. It would also mean that sleep would become important; staying awake for long periods or engaging in physical activity for an extended time would reduce this bar, as would selecting fast travel options like travelling recklessly, if incorporated into the FT system.
This seems like an addition that those thief types would particularly enjoy using, and if implemented properly, would add immersion to the system without encumbering the casual player too much. It also opens the door for all sorts of different characters. You could poison someone's food with a concoction that renders them unconscious, giving you a chance to lift their key without killing them or pickpocketting. Perhaps the Fighter's Guild wants you to bring someone back alive. There are lots of opportunities for using this state.
Thoughts? Suggestions? Comments?