I like to visualize this as a problem of flux balance. For example, let be a CDS payout from party j to i. Then the total net gain or loss (i.e. flux) for party i is given by
We see that the sum over is zero verifying that it is a zero sum game. It actually would be a simple matter to unwind all the obligations if everyone agreed to do it all at once. This could even be done without anyone disclosing any of their trades. People may want to do this so others wouldn't know how weak they were. The way you would do it is for everyone to compute their net flux and disclose this amount to a central clearinghouse. The clearing house then checks to see if the sum of all the fluxes is zero. If the sum is not zero then either someone made a mistake or tried to cheat. If it sums to zero then those with a negative flux would deposit that amount to the clearinghouse and those with a positive flux could then withdraw from it. It is possible to cheat if you collude with someone else so that the net change to the sum of your two fluxes is zero. However, that would not affect anyone else so it would be like a private deal between two parties.