Netting Problem

It is August in a small town on the South Coast of France. Holiday season is in full swing, but it is raining so there is not too much business happening. Everyone is heavily in debt.
Luckily, a rich Russian tourist arrives in the foyer of the small local hotel. He asks for a room and puts a €100 note on the reception counter, takes a key and goes to inspect the room located up the stairs on the third floor.
The hotel owner takes the banknote in a hurry and rushes to his meat supplier to whom he owes €100.
The butcher takes the money and races to his supplier to pay his debt.
The wholesaler rushes to the farmer to pay €100 for pigs he purchased some time ago.
The farmer triumphantly gives the €100 note to a local prostitute who gave him her services on credit.
The prostitute goes quickly to the hotel, as she owed the hotel for her hourly room use to entertain clients. She places the €100 note on the reception counter.
At that moment, the rich Russian is coming down to reception and informs the hotel owner that the proposed room is unsatisfactory and takes his €100 back and departs.
There was neither income nor profit. But everyone no longer has any debt and the small townspeople look optimistically towards their future.

- story borrowed from http://emilie.hermit.net/content/recirculation-funds

The reasoning behind the ocean of derivatives and other financial obligations floating around in the world is that they mostly cancel each other out. That's the excuse because otherwise their amount (arguably some 20 times the total world economy) wouldn't make any sense. It's like adding up all €100 debts from the story above, and arriving at €400 in total debt, all canceled out by one ring of €100 transactions:

1. Hotel Owner's debt to Meat Supplier: €100
2. Meat Supplier's debt to Farmer: €100
3. Farmer's debt to Prostitute: €100
4. Prostitute's debt to Hotel Owner: €100

When €400 becomes €0 after canceling out all transactions, this is called netting. Everything is fine and supposedly there's nothing to worry about. A situation which can be illustrated like this:

Obligations cancel each other out thanks to netting, everyone involved is supposed to win by having their risks managed via a multitude of financial instruments as insurance.

Clearly everything is fine when all people involved have jobs, all loan payments are made on-time, sky is blue and grass is green, and this model is humming along as smoothly any well-oiled machinery. So let's introduce a Devil's Advocate and see what happens. Will the model continue working when the sky is no longer blue or grass is no longer green?
Let's see what happens with the above story when the Meat Supplier decides to take a trip to Greece instead of paying off his debt to the Farmer. Turns out that only €100 in debt gets canceled, leaving €300 still lurking around. And with no way to pay as the income was taken out of the netting universe.
In the world of modern finance, this is precisely the problem that the world is experiencing - failed institutions, failed countries, failed promises, and failed ways to fulfill the promises. Something like this:

Disappearance of a few participants in our formerly ideal circle makes collateral disappear and enormously increases the stress on the rest of the market participants. As the collateral disappears, remaining participants become suspect of not being able to meet their obligations.

So what do you do when the world-as-we-knew-it no longer seems to work? Will you tax the rest of the society to pay off Meat Supplier's debt to the Farmer? I guess in a truly altruistic or kleptocratic society this is possible, and if people decide that they want to subsidize Meat Supplier's vacation time or steal from others to subsidize that, they can do it.
But clearly things are very different when the same happens to the world of financial derivatives. Will the world's taxpayers be altruistic enough to pay off debts that could be measured on the scale of the World's GDP? Or if it's stolen from them forcefully via corruption, would it still be possible? Isn't it completely foolish to even think in that direction?
Or, the same question in other words: what should be the size of EFSF to make it work? 10% of the world's GDP? 20%? 50%? Is it even possible to know the answer to this question???