Bank receives 100 BTCs from A. Bank credits A with 100 BTCs at its bank which can be withdrawn, spent, or transferred at any time.
Bank lends 90 BTCs out to other people as loans.
A withdraws his 100 BTCs <-- They no longer exist.
It cannot do this unless it sells the 90BTC of loans to another party in return for real BTCs which it can then use to back its deposits. It cannot back its deposits with paper, because the depositor does not want paper, he wants BTCs. That's what he agreed to and that's what the bank promised.
Furthermore in the previous post, I claim, if you can do this efficiently you can quickly convert "loan properties" to BTC by quickly selling them to investors on-demand. (in this case investor money means hoarded BTC)
Yes, the bank can now borrow BTCs from another bank in order to pay out the depositor, but a banking system cannot do so in aggregate. Loans need to be backed by savings.
So loans don't need to be "backed by savings" in the sense that there is BTC in a hoarded address. I needs to be backed by an asset liquid enough to be converted back to BTC on-demand. (gold would probably qualify)
The idea sounds plausible but in real life, who would buy that asset if everyone is too busy holding onto their BTC?
For this to work well, the loan to equity value of these assets would have to be very, very small indeed. E.g. a house with a current value of BTC1,000,000 might only be enough security for a BTC300,000 loan in order to cover worse case scenarios.
Also, housing is probably very poor collateral in a nose diving economy - who's looking to buy a house? It would only be investors keen for a bargain but with enough capital to hold onto their investment until after the economy recovered.