.. which is why in the real world central banks are there to act as lenders of last resort. If there's a bank run, print money and lend it to the banks until the run stops.

This is separate from the issues facing stablecoins. I'm reminded of the British government's failed attempt to maintain a "stablepound" against the "stablemark", in the proto-stablecoin mechanism known as the ERM. https://en.wikipedia.org/wiki/Black_Wednesday

Many of the same features are there. Spend the reserves! Increase the interest rates! Ultimately they had to de-peg.

The person on the other side of that trade? George Soros. Yes, really.