What's amazing is that more people don't think this through. They just take the "thin air" story and that's it.
Both Alice and Bob's salaries are just credit at banks in the same system. If they sell their cars they get money from the same system. There's no way out.
The banking system's accounting trick to create money was proven by prof Richard Werner.
The limits on cash transactions are growing. To pay for something like a car you'd need a bag of papers as higher denominations to match inflation would never be printed. Cops can seize cash without much of an excuse. Customs can seize cash over 10k without much of an excuse.
A small bank can only go down if other banks don't trust them. Like SBV a couple of years ago. But their assets are taken by a bigger bank. Lehman Brothers was a rare exception and it looks like Goldman wanted them to go down for some petty reason. But the AIGs will always be bailed out.
More small banks going belly up and more bailouts are coming. The world is reducing exposure to dollar. Central banks are selling US treasuries and buying gold. The US dollar's empire is crashing down and the Western banking cartel is getting desperate. They'll try to drag the world into war or some other old trick.
Money is moved; this is the problem with your analysis, see page 19 of the infamous Bank of England's "How Money is Created" paper [1].
[1]: https://www.bankofengland.co.uk/-/media/boe/files/quarterly-...
There is no magic in banking. If you describe something and it sounds magical, a piece is missing. If you were running bank B, you'd never agree to what you described. You'd want the assets, or you'd want some kind of collateral even if you were willing to do an interbank credit, you'd limit it, you'd do all kinds of credit analysis on your bank counterparties... And what I just described is how trading of securities tends to work between banks. But even then, it's not how payments are solved...