Well, not to spoil the gravity of death, but it's D&D so death isn't quite as permanent as it normally is.
What I'm currently leaning towards is a contest of skills. This isn't Ike suffocating under water, as strangulation cuts off the blood flow to the brain immediately. I'm no MMA fighting fan, but I guess about 12 or so seconds can pass while being strangled before someone looses consciousness. Thats two very intense rounds in game. The first round will be her acrobatics check against his strength plus proficiency. If she wins she breaks the grapple, if not she has one more round to try.
If both rounds she fails, she will find the big sleep.
If she breaks the grapple, anything can happen that she tries, but he's going to try a grapple again.
If anyone has suggestions that make this more fair or exciting, by all means speak up.
Just be prepared for the PCs to adopt this wonderful new combat tactic "I strangle him. If I win two grapple checks, the n HP creature is unconscious!" Even if the situation is limited to starting in non-combat (though I can't see it would -- combat moves often include a choke hold type action) the PCs will find a way to apply it. It's easier to stick to the rules provided: it means the players understand the level of danger and what they can do to mitigate it and leaves the relative balance of the game choices where the designers expected.