What Happens to the Stableswap Invariant If One of the Stablecoins Loses Its Peg Significantly?

If one of the stablecoins loses its peg significantly, the stableswap invariant's behavior shifts away from the constant sum component and closer to the constant product (x y=k) component. This is a deliberate design to prevent the pool from being completely drained of the more valuable, pegged asset.

The curve steepens dramatically, causing high slippage for trades and protecting the remaining liquidity, but also locking in the impermanent loss for LPs.