The answer to the question of whether a DEX can go bankrupt depends on the type of protection that is in place. If the DEX has permanent loss protection, then it is unlikely that it will go bankrupt. This is because the funds are protected from permanent loss due to the smart contracts that are in place. However, if the DEX developers do not have the financial resources to maintain the front end of the DEX, then users may still be able to access the contracts endpoints and trade, but the DEX could still be at risk of bankruptcy. Ultimately, the risk of bankruptcy depends on the type of protection that is in place and the financial resources of the DEX developers.