I'm not a crypto participant, but my understanding is that technically Tether doesn't promise redemption in USD, just backing by USD. That still seems like it could precipitate a crash, but IDK if such a crash would be best described as a run or not.
Tether does offer redemption, but the minimum amount you can redeem is 100,000 USDT, and there is a fee that ranges from 0.1% to 1% depending on the size of the redemption:
So if a well-capitalized arbitrageur can buy a million USDT at a price less than 0.999, they can redeem them for a profit, as long as Tether keeps honoring redemptions.