Why do I ask?
This approach could be one possible solution to the zero bound on interest rates for cash/currency holdings. It would allow longs to pay interest to shorts if and when the market calls for it.
There are possibly other ways of allowing for negative rates that might also be explored. For example, maybe it's possible that when people pay USD from their wallets, a variable "transaction cost" is applied to represent accrued interest owing at that point.
Also note this is no issue at all in bill/bond markets based around zero-coupon bond structures, because negative rates are simply reflected in exchange prices above par.How might this work?
Suppose we had a token called DEPOSIT. People can buy, sell and short DEPOSIT tokens. At any time, a DEPOSIT represents a certain number of USD effectively held in a block-chain deposit account. So a feed price can easily be calculated for the fair value of a DEPOSIT.
However, the number of USD that a DEPOSIT represents is variable. When the interest rate is positive, it goes up, and when it is negative it goes down. On settlement, shorts are only obliged to pay back the same number of DEPOSIT tokens as they shorted, and they do not pay any additional interest, as the interest rate is built into the value of a DEPOSIT in the price feed.
In theory it would be possible for people to exchange DEPOSIT tokens for goods and services. But as they represent a variable basket of USD, this is not the most convenient for pricing such goods. That's where a checking system could be useful. Party A wants to pay for a service from Party B for X USD. So they create X check tokens, sign them and issue them to Party B. Party B sends the check, now signed by both parties, to the block-chain. The block-chain checks that Party A has the USD available, and if not, "bounces" the check. If it does, it calculates the settlement as a certain number of DEPOSIT tokens transferring from Party A to Party B.
[Edit: Maybe the system could prevent Party A from issuing checks in excess of their USD, so avoid bouncing altogether.]