If Tether's USDT went belly up, there would be a loss of confidence in the Coinbase exchange, a run on the market, and a collapse in the price of Bitcoin.
Right now, everyone who has an account at Coinbase believes that if they liquidated their Bitcoin tomorrow, they would eventually get genuine US Dollars equal to the amount of money in their account. Under normal operating conditions, this is true. But if Tether's USDT goes down in price significantly, all bets are off.
Under normal operating conditions, when a client sells Bitcoin in their Coinbase account, Coinbase trades Bitcoin for Tether's USDT, the USDT sits in the user's account for a while, and eventually the user get US Dollars.
Where do the US Dollars come from?
Tether has a reserve of some US Dollars, and other non-crypto assets that can be quickly traded for US Dollars. Let's just consider this whole bucket as US Dollar reserves in order to simplify this discussion. The important thing to remember is that Tether's US Dollar reserves are only a small fraction of all outstanding Tethers.
Also, Tether is constantly gathering more US Dollars. On an average day, Tether receives more US Dollars than go out.
If for some reason, everyone decided at the same time that a USDT was worth less that one US Dollar and the price continued to drop over time, everything would change. In this dropping USDT price scenario, anyone who held USDT would go to Tether at the same time and ask for their US Dollars back.
Tether would have a few options at this point, but one option they would not have is giving everyone their US Dollars back. Remember that Tether has limited US Dollar reserves. Assuming they kept trying to refund every request with a full US Dollar, they would blow through their reserve and hang up a closed sign on their window. Tether doesn't have any bankruptcy insurance, and there isn't a government that is likely to bail Tether out. They're not too big to fail.
Oh, Tether would try some tricks to slow down the process. But they may not be able to stop the run on the bank/exchange.
So now, let's assume Tether is worth zero. What happens to Coinbase and it's clients?
Buying Bitcoin would not be a huge problem. Coinbase might have to change their procedures, but they could still find people willing to accept US Dollars in return for Bitcoin.
The trouble would be selling Bitcoin. On a normal day, they just trade Bitcoin for USDT, and if necessary, go to Tether and trade the USDT for US Dollars. But if the normal system doesn't work because a USDT is worth zero, Coinbase would have trouble selling Bitcoin in a timely manner.
People would flood Twitter complaining that they can't get their money out of Bitcoin through Coinbase, and this might trigger a second run. All Coinbase customers might lose confidence at the same time, and try to sell their Bitcoin in their Coinbase accounts at the same time. The price of Bitcoin would crash. Perhaps people would not trust exchanges such as Coinbase for a long time after, and prices might stay low for a long time.
This is all just a wild guess. What do I know?