I wouldn't have to ID you.
Say:
You deposit X BTC.
You open a position for Y BTC/USD.
BTC/USD goes down a little so your position is only worth (Y-X).
I liquidate your position.
Now mtgox has (Y-X) + X which = Y which is the amount of the loan.
The exchange hasn't lost anything so I don't need to know who you are.
I get how it works when there enough bids at the right prices. But how is this guaranteed?
The bid will be put automagically by Mt. Gox whenever someone do this kid of trading. The price isn't going to fall below that bid until everything has been bought at that price by someone. If the price stops there or rises again, no problem.