The question came up recently - what happens if one side of the complication is at 0 or less dice at the time everyone decides to resolve?

Is it just 0? 

The recent example had a character with several traits against him, so much so that he ended up being drawn against down to what amounted to negative two dice.  The owner of the character was almost spent out.

Interesting question.  It's never come up in any game I've played...and I'm pretty sure there's no explicit answer in the book for that.

If it came up in play I would definitely recommend not going to negative dice, as that has no value for either player.  Just use the option to add your opponent's disadvantage to your own Dice Pool.  Was everyone aware they could do that?  Since you generate more Coins by adding the die to your own pool, that's the most common thing players will do unless they absolutely positively don't want the other side to have a say in what happens.

In that case, if you're the side with zero dice...you're pretty much hosed.  You'll lose with no Coins gained.

Can you give me the specifics (including who grabbed what Traits and when)? I'm having trouble envisioning the scenario where this would happen at the table as anything more than very unusual...

There's also the Gimmick where you don't allow reduction of dice, but only the add dice to opponents feature if you find it happening more often. 

Sure - we had Mitch and the Russian Partisans.  Both had just lost a complication against the Uberfaust, a magical hell-fire throwing nazi tank which added moral lowering traits.  Its in the middle of a blizzard.  One player who controlled Mitch and the Partisans had Mitch lead the Partisans in his plan to lure the tank onto some ice.  Another player (me!) interrupted, takin control of the partisans to try to convince Mitch to abandon his plan and seek shelter from the blizzard, creating a complication.

So the complication starts out looking like this (all drawn by me):

LL: Russian Partisans: moral is at an all time low, images haunt them, have had enough of the battlefield. Russian Front: frozen landscape, frigid weather, low visibility x3. 8 dice.

QS: Mitch: "Mitch," (drawn against) fatalistic outlook, (drawn against) feels some responsibility towards the russians he works with, (drawn against) images haunt him. NEGATIVE 2 dice so far.