Tether the company guarantees it will buy all tether for $1 each. The drop in price reflects people suddenly realizing they can’t do that if everyone tries to turn in their tether at once.
Even national governments struggle to do this. https://en.wikipedia.org/wiki/Black_Wednesday
Now, of course, if you decided to _not_ be open and _not_ hold your reserves in safe assets but instead decided to invest the reserves to speculative gambling tokens or shady commercial papers, then it really is difficult to keep the guarantee if the gambling token loses value.
A price is just an abstraction for the willingness to buy and sell. If you know there are 1000 of some token in the world, and you have 1000 of some item, you can guarantee that people will always be able to buy one item for one token - by selling your items to them at that price.
But of course, just holding the dollars makes it hard to profit.
I don't think the Black Wednesday situation is similar, because the UK was never going to be able to hold enough of the currencies it was supposedly pegged to to make that same promise. Definitely not my expertise there though!