Looking at the Suffocation rules on page 269, it looks like there isn't a way for someone to die through strangulation alone.
The rules (paraphrased): A suffocating character suffers fatigue each round, but specifically does not suffer critical strikes from those wounds. If the character is Unconscious at the start of a turn in which they're suffocating, then they make a check to avoid death. But while fatigue can give a character the Incapacitated condition, an Incapacitated character only becomes Unconscious if they suffer a critical strike (which suffocation explicitly does not do).
Seems like there's an oversight here. Maybe the suffocation rules meant to specify Incapacitated rather than Unconscious? Has anyone run into this in a game, and if so, how did you run it?