It would be like a bank where you only put in cash and the deposit envelopes are never opened and the money all thrown in the same pile. Your bank statement would be just the series of deposits and withdrawals. When a withdrawal is made, you select enough of the (former) deposit envelopes to cover the payment and send them all, unopened to the payee. The payee accepts all the ones that can be accepted whole, and opens only the last one to make up the last bit, taking the remaining money, stuffing it a new deposit envelope and sending it to you as change.
Is that right? Seems at some point you have to break open an envelope and make a new one or you'd have a series of change request flying back and forth indefinitely.
Yeah, not bad. But it isn't the payee opening the envelopes and making change, it is the payer. And there is no bank, but the whole world is watching you open your envelopes and makes sure that you don't put more in your output envelopes than you took out of your input envelopes.