It's just game theory. Lets suppose you want to accept an IOU from some identity, a good example would be a digital bearer certificate issued as part of a microtransactions or chaum-based coin-swapping system. To know if you should accept that debt from the identity you need to be able to figure out the value of the identity, determine how much the identity owes others in total, and be able to publicly prove the identity has done something wrong to destroy it's reputation. My proposal allows you to solve the first problem by providing a way of assigning a known value to the identity.

Suppose you, Alice, want to know if you should accept a 0.001BTC micro-transaction certificate issued by "Bob" as payment. You know (somehow) that the total value of all such certificates issued at this time is 10BTC. Bob has used the above mechanism to provably throw away 100BTC of value. Thus if Bob simply keeps all his deposits he'll get to keep the 10BTC of deposits, but he's thrown away a reputation that cost him 100BTC to aquire. Thus it's in his interest to honor the deposit certificates.

What's nice about this proposal is that the proof of value is just a list of transaction pairs, and if you include the merkle paths up to the block header even SPV clients can validate the proof. You can also make these reputations securely exchangeable by using their outputs as smartcoins, and again SPV clients can validate the proof by giving them the transaction history - if a "reputation" can be sold it means that an identity that wants to shutdown a service still has an incentive to pay back outstanding debts because the reputation still has value. (although you'll need to limit what the reputation can be used for, see below)

Of course, the value assignment is the easy part... Creating efficient mechanisms for determining the total amount of outstanding debt as well as ways of publicly publishing and automatically validating proofs of wrong doing is much more complex and will depend on exactly what sort of transaction is being done. (similar to what OpenTransactions attempts to solve) Either way this mechanism will work best if people can agree on one way to do it, and helps strengthen security by promoting mining too.