Well, Bitfinex and Tether is how legacy exchanges operate. Bitfinex is completely centralized and issues Tether (a stable coin) as a feature to enable traders to do "cash out" from the volatility of crypto when they feel like.

Going forward though there will be dexes and decentralized stable coins (such as Basecoin). Those would be extremely difficult to track down and have strong incentive structures to maintain their value.