I tested this with Unbreaking III on a pickaxe and it seems that when it reaches "0" durability you can still use the tools quite a few times, more than you could previously.

EDIT: I spawned a pickaxe with 1 point of durability and enchanted it with Unbreaking III and from what I can see the amount of blocks I can mine before the tool breaks is different everytime. One time I could mine 9 blocks of dirt, the other time, only 6 blocks of stone. Should that be the case?