If the government were to take a real close look at their books, there would be very few institutions immune from bankruptcy. These companies engage in risky business practices all for a quick profit and then expect bailouts even though they can pay millions in bonuses. I wish the government would investigate the lot of them.
Look at Lehman Brothers, and you'll see that even with that example, Wall Street is just about as reckless as ever. I'm sure some of the institutions are carrying a lot of debt and at risk for bankruptcy. Without some major financial changes that will probably continue to be the case.
Yes, the major institutions are at risk for bankruptcy because the stock market goes back and forth. No one knows what will happen tomorrow on Wall Street. All companies should be prepared for failure, no matter how high they might be. Tomorrow could change the landscape in either direction for these companies.
Major financial institutions are currently not at risk for bankruptcy. These institutions have had to markedly increase their capital since the financial meltdown a few years ago. Management at these large banks have also gotten more cautious. There are governmental auditors that regularly check to ensure the safety of the companies.