A character is on the run. Very likely, he's been part of a Stern Chase
from the word go. The logical course of action would be to do whatever he has to do, while drawing the least amount of attention to himself he possibly can.
He won't consider it for a moment.
That random stranger over there needs help, and he won't stand idly by for the sake of anonymity.
Often leads to detection by the people he's been evading all this time
, but not as often as you'd think.
- Jean Valjean from Les MisÚrables is, of course, the Trope Namer. More often than not, his Moments involved throwing himself directly in Inspector Javert's path, rather than merely risking the same.
- Kenzou Tenma from Monster will never let an injury go uncared-for. Ever. At one point, an unscrupulous character wanted to recruit him as an underground physician, but really, that's a good part of what he was doing already.
- In Firefly, Simon Tam, amid breaking into an Alliance hospital, stopped to save a man's life from his doctor's incometence.
- In Harry Potter and the Deathly Hallows, the Trio enacted an impromptu mass breakout of Muggle-borns on the way to pick up a MacGuffin from one of the densest centers of Death Eater activity.