Another question that someone else posed and I attempted to answer. What came to mind for me was cases where a player decides, of their own volition, to keep an NPC safe when they could easily have let them die instead (and the GM/game designer likely expected them to), and the amazing dedication they can show when pursuing this self-determined goal (as opposed to the utter frustration people feel towards escort missions).
I'd frame it as a subversion, similar to fathom. You could do a 2-D side-scrolling action game with a B-movie feel, reminiscent of Metal Slug. The level opens with a shot of a diner, then monsters burst in and start wreaking havoc. Pan left (with "GO!" flashing several times, big enough to fill the screen) and we see your character emerging from the bathroom, with an exclamation point appearing over their heads as they see said havoc spill into view. A bouncing arrow points out a shotgun to the left, so you grab that and then use it (along with a jumping kick attack) to fight your way out of the diner and down the hill to an oversized boss. Except that when the boss dies, the music just stops. We see the character walk offscreen back towards the diner, cutting back to the back hallway where we first started playing. He walks over to the body of one of those background NPCs from the intro, and shows some kind of grief- whatever body language and gestures prove the most expressive for the character model. Fade to black.
If you play the game again, you'll likely notice that the woman in question dies *after* you gain control of the character, in what looked like a scripted event. And if your first action is to run to the right and attack the monster with your difficult-but-functional kick attack (which the game doesn't tell you about for another 20 seconds, so you don't know about it your first time through), instead of grabbing the shotgun first, you can actually save that character, and continue to defend them as you fight through the rest of the level. They'll die if any monster gets to them, making it very difficult to make it through to the end of the game without them dying; but it's still possible.
Perhaps you'd actually expand on the gameplay- every section of the game sees the woman doing something else while you fight the monsters, changing how you play during that section. She'd interact with elements of the apparently-static background, demonstrating alot of resourcefulness and ingenuity (though not any combat prowess). It's important to note that her efforts to help herself and you never make the game easier; they just create another slim window of opportunity for you to keep the two of you alive a little longer, and by extension give the game experience noticeable variety.
I'm not doing this because I have any love for the "damsel in distress" option, I'm doing it to deliberately remove outside incentives- where there's no rational reason to shoulder all this hardship except that you care about what happens to this person, damn it. And when you stick with that approach, you wind up getting alot more out of a life that used to be much more effortless and predictable.