A solo survivor
The problem with Left Behind and Sole Survivor are the same: premised on being the last survivor left. Imagine what kind of great altruism that promotes (sarcasm).
I'm saying that the current goal for many survivors is to get everyone out alive, but the goal as first envisioned and implemented by the devs was for a survivor to get him/herself out alive and not need to worry about getting someone else out--that part was optional. I bought the game under the latter impression, and I've slowly realized that most players play differently from that because of how the game forced the survivors to change.
Just as some mild back up, take a look at how many perks there are in the game for survivors to have information on where each other are in addition to how many perks encourage and facilitate survivors helping others. Those perks were supposed to make an almost definitely unrewarding action rewarding (eg. No One Left Behind), but now the perks make necessary actions (like healing other survivors and performing unhooks) easier.
If I don't unhook a survivor or heal an injured teammate when I have spare time, I am certainly going to die (excluding very specific circumstances).
I made my post just so that newcomers to DbD who read your comment weren't under the impression that it's a given that the goal is to get all the survivors out alive, because it's not exactly hard fact. The killer and survivors have conflicting goals, but not entirely opposing. That's why the biggest balance issues occur in this game when survivors go out of their ways to help another survivor live.
Oh okay. I might try it if they fix Sole Survivor.
... Do not.
I don't think it should be a perk. Though it would make a really nice game play over all. As survivors drop, the entity makes it more challenging/interesting. After all its one big game to the entity.