Think of the stablecoin as an ETF. If people need to launder money or take advantage of a programmatic bug, that would raise the stablecoin price over $1.

By default, I'd imagine the reduced liquidity and counterparty risk (relative to dollars) would cause the stablecoin to trade at a discount to cash, particularly when auctioned by the government. (You have to spend resources monitoring the auction, closing the transaction, and cashing out to complete the arbitrage.)