RAW: it doesn't say.Hello,
What happens to a character that has zero healing surges when he is hit by an attack that causes him to lose a healing surge?
Thanks.
You could rule that, if you're supposed to lose a healing surge, lose the healing surge value in hp.
Just to pitch in my 2 cp:
I think that, by the time your healing surges are depleted, you've probably been punished enough. If you don't have a surge to lose, don't lose it. If they're truly getting into the game, they should be worried enough by the time they reach that point.
As for losing the surge value in hp, though, be careful about punishing Dragonborn for having high Constitution. You might keep it a static value (5 per tier?) so that ANY characters with higher Con aren't punished for being more durable, either.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.