Luckily for Paolo & friends, their terms of service clearly state that they do not ever have to offer redemptions of USDT for dollars. Or even whatever IOUs and bits of string they may or may not have in reserve.
Out of all the stable coins its the most likely to withstand a "run" because they do not have to pay you if you ask. In fact if you're a US person, you're not eligible at all. If you're not a US person, it's at their discretion to deem you a "customer." Even if they do that, they can delay your withdrawal arbitrarily. Even if they don't do that, they can pay you out with whatever is actually in their backing. [1]
What would get destroyed in a run is every other crypto, as folks desperately try and exchange their USDT for something they can sell at a fiat-backed exchange. The Crypto-USDT pairs will quickly go no-bid, and as people rush for the narrow exits at fiat exchanges, prices will plummet.
[1] tether.to/legal