A stable coin doesn’t necessarily have to be backed by fiat, DAI is backed by crypto assets and those assets can fluctuate and sometimes need to be increased during volatility.

I think the point of fiat backed stable coins are more for getting around regulations (eg Tether) and a fiat on-ramp for getting into the ecosystem. Certainly if the government seized a large portion of Tethers assets then that could affect other assets, but this actually has already happened with (a small portion, not large) Tether and nothing catastrophic happened.