@Blitzpaw I have to say that this is a very interesting concept!
it probably is difficult to do this without it being gimmicky, but maybe you could try to give them permanent concequences. (I don´t know what world this is set in, so I´ll give just a few examples)
maybe a bullet to the head went straight through, they survived (If I remember correctly there have been cases of this), but a part of their brain got permanently damaged (Maybe they don´t feel pain anymore, or they lost their eyesight)
an arrow close to the heart was removed, but the tip couldn´t be retrieved and they have physical pain that makes it impossible for the to do their usual style of fighting, so they have to change their tactics.
a limb got removed and they are out of the picture for like two years or more, building a prosthetic as best they can, that still isn´t perfect, or maybe just crutches (and don´t forget about phantom pain).
you can always add (depending on your level of magic/Sci-fi elements) new powers, if you take strengths they preveously had away from them.
!!! with that being said, I strongly reccomend doing research about these cases in which fatal wounds were survived, because some sort of realism is definitely good in these instances, and what concequences these injuries have !!!
also always give them time to recover, and heal especially, because really, they should´ve died long ago. they just are incredibly lucky.
But yeah, that´s all I can think of at the moment, I hope you can work with that.
also their drive to survive probably is to get back at those who have wounded them.
So good luck writing them, and if you have further questions you can always message me :)