It's simpler than you are imagining. In practice, anyone can make USD go in one side and EUR come out the other. It's just the notion that something is "destroyed" which is wrong. If I owe you x USD, you can call me and we can agree I now owe you y EUR. If my name is "JP Morgan Chase Bank", it's really easy. And, the "m1 money supply" just changed. But, m1 is kind of nonsense because... it includes checking account deposits which are just IOUs from banks. So, no one just got richer (the bank still owes you money) and nothing is really going on.

Your mental model is falling down around the definition of "currency", "money" etc. It isn't what you imagine it is. We just have a system for trading bank receivables and call it "money".