So I tend to have rogue-heavy groups (no idea why) and this has come up before. I've got this rule going for the scenario.
Dex (Stealth) check vs. passive perception to get in position, disadvantaged Attack roll to get the knife in place. Since they have Advantage from their Stealth attack, it works out to a normal attack. Assassins have Advantage on this attack roll.
If they succeed the target is Grappled and has the knife pressed to their throat. If the attacker takes any action, even a free action, that requires the use of a hand the target may make an attempt to escape as if escaping a grapple, but succeed or fail they take damage as if hit by a sneak attack.
If they fail, they do not land a hit, the target becomes aware of them, and the target may immediately use a reaction to make an Attack or Grapple if they wish.
From that point, the knife-holder can use a Bonus action or Reaction to slit the target's throat. The target gets to make a Str or Dex save vs. the knife-holder's original attack roll to avoid instantly dropping to 0hp.
On success they only suffer a critical hit plus SA damage if applicable.
If something is helping the target avoid damage (eg. a non-armor throat protection, or something distracting the attacker) they gain advantage on their save.
There's never never ever advantage for AC-granting armor like platemail or a chain shirt, no matter how much your players point out that those armors included neck protection. Since AC affects the initial attack roll's difficulty, this has already been taken into account.
The end result is a high risk but very high reward move, that potentially ends up with the rogue alone, grappled, and having used their attack directly adjacent to a powerful enemy whose turn is coming up. It's a bit riskier than a normal surprise attack because of the lack of advantage and provoked attack, but it guarantees at least a critical hit if it succeeds. (That's why Assassins get Advantage, since they could already get a guaranteed crit without any extra risk)
I make sure to enforce various rules about needing cover to pull this off, so they can't just "sneak" through an open room and one-shot BBEGs.
The fact that targets drop to 0hp and don't instantly die makes this usable against PC's and BBEG's because of the possibility that a well-timed healing spell or medical attention might save them.
The inclusion of SA damage and Assassin advantage makes sure that these character types don't lose their awesomeness because of this extra rule.