In order to maintain the peg, we limit trades that may weaken the peg indirectly
So basically, it should be illiquid. This is a very old post about the topic.
Onchain/LN liabilities + Perpetual Futures are probably more robust than that.
This is what we have done in Valet initially. Currently, we are hedging our liabilities on the spot market. Unfortunately, perps are very KYC-ed, or otherwise, exchanges aren't liquid enough.