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You've sort of got the group of tropes already here, though I'll also throw in:
- Heroic Safe Mode - they just mentally check out and operate in survival mode for a while
- Rage Breaking Point - the last floodgate holding back a character's rage breaks
- Run or Die - the flight portion of fight or flight can be just as desperate
- Dying Moment of Awesome when it's their own hope of survival that they've lost
- The Unfettered - what you get when everything that would hold a character back has been removed.
I think maybe there could be a supertrope, or at least an index, in Nothing Left To Lose, but it's one that might be hard to pin down.
- Heroic Safe Mode doesn't count, that's explicitly pulled out WHILE things are still at stake, not AFTER the stakes have already been lost.
- Rage Breaking Point doesn't count, it exists independently of anything at stake, e.g. a character can erupt over something as minor as a teammate popping gum or one too many questions of "Are We There Yet?" as they march towards their next climactic battle with the forces of Emperor Evulz.
- Run or Die: I'm not sure this counts, it doesn't even mention the possibility of being able to run faster when running is the only option left.
Your second example is a good example of a situation that can lead to both Heroic Safe Mode and Rage Breaking Point- the final hostage being the one that causes them to snap and go into survival mode, and/or the moment that removes any reason to hold back.
For Run or Die, it's exactly like Cornered Rattlesnake. It's not that the situation gives you an advantage per-say: it's that having your options reduced to "fight, run, or die" means you have nothing to lose putting everything you've got into one or both of first two.
Edited by Scorpion451Bump: added more examples to the list
If not for this anchor I'd be dancing between the stars. At least I can try to write better vampire stories than Twilight.

The more of what's at stake is lost, the more some sort of twisted advantage is gained from having already lost it. Do we have a super-trope, a group of tropes, or an index that covers this concept and/or specific examples of this concept?
- Dying Moment of Awesome and The Last Dance: The less life you have left, the more you can risk it as you Do Not Go Gentle.
- The villain has a group of hostages and is slowly killing them off one by one. The hero Ain't Too Proud to Beg and dance to the villain's tune for as long as at least one hostage is alive, but the instant the villain runs out of hostages to kill, the hero goes on a Roaring Rampage of Revenge.
- Too Broken to Break
: The more traumatized someone is, the more they're immune to further attempts to traumatize them.
- Cornered Rattlesnake: With no escape left but over the enemy's dead body, suddenly you find yourself fighting better than you've ever fought before.
- Run or Die: When there's nothing left to do but run, you find yourself running faster than you've ever run before.
- The Unfettered: Among other potential causes, this is what you get when everything that would hold a character back has been removed.
- Situations on Blackmail Backfire:
- The victim decides that the blackmailer's terms are worse than having the information publicized, and may even reveal the information themselves.
- The victim has been so ruined by their life experience that he or she has nothing left to lose and only wants one thing: Revenge (or at least to stop the blackmailer in his/her tracks).
Edited by Miss_Desperado