Nothing per the rules though a common houserule would be based on the starvation, thirst, and suffocation rule: "A character without healing surges who fails a check takes damage equal to his level."
Hello,
What happens when a Deathlock Wight damages you with a claw attack but you have no healing surges left to lose?
Anything?
Huh... I always thought the 'take damage equal to your healing surge value' was the actual rule. Anyway, that's the house rule I would use, though I've honestly never had it come up. I don't often use monsters that hit for surges.