Well Bitfinex is a special case relating to Tether, but I'm sure all exchanges hold some amount of money in some way to support operations. It's just misunderstanding how exchanges work to think a price drop in a thing being traded puts exchanges at risk.

It would only do so if the exchange has a strange unrelated agreement (like to trade 1 USDT for 1 USD), or were holding the money they're using to run their operation in that asset. Except for maybe Bitfinex (because of the special case), no exchanges are doing that with USDT.