A mechanic where you don’t always fall instantly - maybe if you press a "save" key at just the right moment, you can grab onto a rope. Then your friend can run over and help pull you back up, or, if things go wrong (or on purpose), you might drag them down into the abyss with you. I think that would be fun.
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I’m not sure. There should probably be a way to save yourself, but it should be much harder than being helped by a teammate. Maybe a successful self-recovery would require perfectly inputting a specific button sequence or completing some kind of mini-game.
If you try to save yourself, the challenge should be longer or more difficult. But when a teammate helps, the task becomes easier or shorter - though both players still need to participate. Depending on how well both players perform, you could recover, fall, or even both fall together (if one of the players completely fails), causing the overall success level to drop critically.