The original owner doesn't hold the shares either, but they do have a contract for them to be returned.
As a practical matter, this effectively creates shares, just like a bank loaning money creates money.
If a short seller decides, today, that they no longer want to involved with this stock at all and, simultaneously, by pure coincidence, the person they borrowed the share from decides that they also don't want to be involved with this stock at all so they both close their positions and settle up. The third person out on the market keeps owning the share that they never knew was borrowed at all, and everything stays exactly stable. One 'long' dropped out of the market but it had no effect on anything because the 'short' also dropped out at the same time.
That's not what happens when someone takes their money out of the bank and converts them to Benjamins: there is less money available to lend which raises the interest rate somewhat. That's an actual effect!
IIUC the main difference with stock is the market prices the items by demand unlike where the treasury effectively prices the items by supply and banks work under that. So the stocks are expected to always be liquid potentially at a lower price while banks have to be bailed out by the government for liquidity if a bank run. This definitely feels different, though I guess the extreme case gets closer, if every single bank needs to be bailed out at once, the currency price will go down like stocks do.