Letting a bank or another financial institution going broke is difficult. If a normal company goes broke there will be a lot of assets. Maybe they can go on producing for years under the protection of Chapter 11. With financial institutions that is not the case. As soon as it is clear that it may not survive every customer will try to withdraw his money. Soon it will run out of cash and it will go broke for that reason.
For that reason there are special regulations that allow governments to take over banks that are in trouble. However, in the recent crisis these regulations proved to be inadequate, specially when it comes to other financial institutions than banks.
Take Lehman Brothers, whose bankruptcy started the crisis. In a recent article in the Economist the authors argue that Lehman had a deficit of about 25 billion dollar. However, the bankruptcy is resulted in additional damage so that the total cost came to 150 billion dollar. This could have been prevented if there had been a financial authority with the power of a bankruptcy judge. He could have imposed a solution where the shareholders lost all there money while the bondholders lost some of their money and became shareholders. This is the same kind of solution that would have been imposed by a judge in a bankruptcy case. However, such a financial authority should be able to impose it within one or two days. In the months that it takes for a normal bankruptcy judge the company would have become worthless.
A similar case applies to AIG. The US Secretary of the Treasury Geithner is often criticized that the US government took over all the debts of this insurer. It would have been more normal to pay only a certain percentage of the debt (in the financial lingo this is called "giving the debtors a haircut"). Geithner argued that it would have taken a long time to get all debtors to agree to a haircut and that for that reason he had no choice. Here to it would be logical to give some financial authority the power to impose such solutions.
The Obama administration is aiming to establish such a resolution authority.