I don’t think you addressed this to me, but I’ll take a stab.
At a commercial bank, deposits are a liability against the bank. A customer’s account is the amount it owes the customer. So it’s a debt (to you, the customer).
So suppose you take out a loan from ABC bank. The bank credits the amount of the loan to your account. Where does the money come from? The bank just types the amount into its computer.
It’s liabilities have now increased by the amount it just credited to your account.
But banks have balance sheets. And in order for banks to keep being banks, their balance sheets have to balance.
So what do they do?
They enter another number, on the other side of the ledger - the “asset” side. That number is the number the bank thinks the loan it just made to you is worth.
So say the loan was for $100k, plus interest, of course, so that in the course of paying back the loan, you’ll pay the bank $300k, over however many years. That loan - your promise to pay $300k over x number of years - has value. Lets say the value of that loan - it’s present discount value - is $120k. So now the bank’s books balance. On the liability side is $100k - the amount that was added to your account. On the asset side is $120k - the present value of the loan. The banks assets exceed its liabilities by $20k, which means its in good shape. The value of its portfolio is $20k.
The Fed is similar, except that when it “loans” money, it uses the money to buy securities - like, for example that loan currently owned by ABC bank. Or more realistically, it purchases Treasury bonds. The Fed types a number into its computer, sufficient to buy the bond. That number represents a numbe of dollars. That number goes on the liability side. On the asset side the Fed puts the value of the bond.
If the Fed ever wants to “pay back” the loan, all it has to do is sell the Treasury bond back to whoever wants to buy it. The Fed does not HAVE to sell the bond. It could just hold onto it if it wants. But as a practical matter, the Fed does buy and sell bonds all the time, depending whatever policies its trying to pursue.
In any event, the important part, at least in terms of perception, is that the Fed’s assets - all those securities it owns - are worth at least as much as its liabilities - which is the balance in Federal Reserve accounts, plus US currency.
Maybe that doesn’t help much, but to try to answer your question, the Fed is solvent - in fact, it churns out billions of profit every year. If the Fed weren’t solvent, it wouldn’t really matter in a practical sense, except that it would scare the bejesus out people. It would affect public perception of the value of our money, and the fundamental health of our economy and banking system.
And I would further argue, that when it comes to money, perception is everything. That last thing the Fed wants, or anyone wants, is for there to be some sort of financial panic, because the Fed was “bankrupt”.
So I would argue the Fed’s liabilities are “real” in the important and limited sense that it has a powerful incentive to make sure it can show it CAN pay off its “debts”, even if there’s no reason why it would ever need to. (And in fact, it would be a total disaster of it did.)
Again, it’s about perception. The Fed cannot literally go bankrupt in the sense of GM or AOL, or any private company.