Unless, Stable coin providers allow cross transactions of dollars, say USDT be accepted as equivalent to USDC, USDP, FDUSD, USD1 regardless of he network, there will be a liquidity problem similar to a bankrun.
As long as the stable coin can be redeemed for dollars 1:1 the market is "safe". However, if the reserves are not as liquid as to accomodate larger than expected outflows the panic will destabilize the market and cause the collapse of many of those providers, the same way other banks and institutions have gone bankrupt in the past.
Does Anyone remember why Silver Bank collapsed (2023)? The main reason was a massive outflows.
It can happen to any bank and MBS.