All "resolve+composure" rolls are substituted with "willpower rolls". Because "willpower" is calculated based on 'resolve+composure' the consequences are minor. The consequence that do exist, and the reason for this rule, is that it now matters if your "permanent willpower" is lowered for some reason.
YOU GAIN WILLPOWER POINTS...
1) By approaching your core aspiration (ALL)
2) By acting according to your virtue (THREE)
3) By acting according to your vice (ONE)
4) By retaining selfcontrol through chaos (ONE)
5) By having seven hours of undisturbed rest (ONE)
YOU CAN SPEND WILLPOWER POINTS...
1) On a +3 bonus to most dicepools, except resistance! On a
resistance trait you'll gain a +2 bonus! (CofD, p. 73)
2) To substitute for loosing Integrity points when face
to face with unnatural as well as mundane horrors!
3) On fueling "merits" and "powers" when needed! (RTR)
A character without any willpower points remaining is mentally and emotionally exhausted and will act in accordance with the characters nature i.e. virtue & vice.