Overdoing

That stubborn whumpee that won't stop, until their wounds starts bleeding again, or they collapse from exhaustion and have to be tended to by the caretakers and loved ones. Of course there's also the possibility that they're are alone, which opens up a roll of other delicious tropes.

Or who know, perhaps they continue pushing until they make a mistake in the middle of a critic situation and end up even more injured.

Animes
Akatsuki no Yona


 * Ep 6: Hak is shot with a poisoned arrow, but keeps fighting. Blurry vision, sweat. A false move gives the advantage to the enemy, who cuts him across the chest, and Hak falls of the cliff with the blow.
 * Ep 11: Hak helps Ki-ja fight some road bandits, and reopens his injuries, collapsing. Unconscious, he is carried by the other.
 * Ep 14: Ki-ja suddenly collapses from exhaustion after the events at the tunnels, supposedly from digging for an extended period of time.

Dororo


 * Eps 05/06: Even still injured from a previous battle (and weakened by a fever), Hyakkimaru engajes on a fight with another demon. He gains back his voice, but his human leg is ripped off by the enemy. The old priest helps him get back to Mio's house, where she takes care of him.

Tv Shows
Arrow


 * 1x12: Oliver Queen (Stephen Amell) was injected with a powerful drug and almost overdoses, but refuses to stay still. Some scenes of him feeling dizzy, collapsing, and having to be supported by Diggle.

Hanna


 * 1x08: Erik was shot few episodes back, and hadn't stopped since. His wound keeps bleeding (and he keeps hiding it), he gets progressively paler, but keeps fighting anyway.

The Boys


 * 2x08: Hughie's injury (impaled by a metal piece) from the previous episode starts bleeding again with all the running he does while searching for Annie.

Young Wallander


 * 1x02: Kurt leaves the hospital sooner than he should, in order to keep working on the case. Of course his stab wound would start bleeding through his shirt. Lovely care scene.