There cannot be a run on the federal reserve bank since they can simply print at well.
The “run” would be a bit different than your typical Bank Run.
Globally, the world would be rushing to sell their dollars to buy something else like Euros, Yen, Pounds, Oil, Gold, or Silver.
They’d print up a hyperinflation mess like Germany 1922-1923.
Inflation causes long-term interest rates to spike even more upward and thus their holdings of Treasuries/MBS will fall much further in value & they’ll get deeper in the hole.
We’ve seen this type of run hit many fiat currencies. For example, Zimbabwe.
The root cause of this problem is that the United States Congress keeps raising the Debt Ceiling and Deficit Spending. If they would start living within their means then the supply of these bonds would go down, inflation would go away, interest rates would stay low, and the Federal Reserve balance sheet would be able to be above water again, and they’d be able to shrink the balance sheet size. It’s so absurd how the size of their holdings of Treasuries/MBS is over 8 trillion dollars or nearly the entire annual amount of all US worker’ gross wages (approx 9.7 trillion). The people who have been leading Congress this past generation have been very poor leaders. We need some good leaders in Congress ASAP.