The Federal Reserve operates like any other bank with the exception that there is no regulatory limit on how big it’s balance sheet can get relative to the capital invested. In this case the capital comes from the member banks which are required to deposit 1/2 of their investment and make the other half available in case it is called. The banks are guaranteed 8% return on the total amount.

The large balance sheet and small reserves means that the Federal Reserve is thinly capitalized relative to other banks. Forgiving or writing off a loan would result in a loss which should result in the member banks taking a loss. To many losses and Congress would need to chip in to cover losses.

In practice the Treasury will allow the Fed to take a bit of interest from other investment to offset losses. This doesn’t make congress happy because it is effectively redistribution of taxpayer money outside of Congress. Taken to an extreme the Treasury could direct billions of dollars of taxpayer money through bailouts to connected individuals by paying above market prices for assets.

In a pinch the Federal Reserve could also re-value its gold reserves to balance its books and make up for losses. Or it could simply never recognize the losses. For example making a 100 year loan with no interest to the state of Illinois.

Crossing some of these lines would quickly (if not already) trigger a collapse in the currency or a Congressional showdown.