The Federal Reserve wouldn't default. It doesn't owe anyone money. It buys bonds (printing money out of thin air) at favorable interest rates from the US Government.
The US Government defaulting wouldn't impact the Fed's ability to continue to buy infinite sums of assets.
There's no reason that the US Government couldn't default and the Fed buy absurd amounts of treasuries until interest rates remain low or go even lower.
Well, there is sovereign default but if the US does that, then we'd better hold on tightly to our breeches, from Kamchatka to Patagonia.