The Fed isn't on "fractional reserve". The Fed runs on a "no-reserve" basis.
However, there are two primary economic components to all banks, including the Fed: capital and credit
Most banks have a limited ability to supply credit because they are on a fractional reserve system. (Full reserve has even more limited ability to supply credit. "no-reserve" has unlimited ability to supply credit.) If a bank runs out of credit, then it can not issue more loans. However, that does not mean the bank is insolvent.
Capital, on the other hand, is assets minus liabilities. Every time a bank prints money and takes on a loan (or some other asset), the money it printed is a liability and the loan it took on is an asset. When loans fail (or other assets held by the bank lose value), a bank's capital is reduced. When a bank's capital drops below zero, the bank is insolvent.
With the Fed (as with any other bank), if its capital goes below zero (i.e., it goes insolvent) it can't just fix that by printing money. That's because the Fed can only print money to buy stuff -- not to fix its balance sheet.