It hasn't happened (much? ever?), but presumably they would have to buy more stock. But they have other tools: they could cut the member bank dividend (who would complain?), for instance. There's also the possibility of a carry-forward of any losses against future gains to be paid to Treasury.
There's some detail here, though I don't think people like to talk about it much :-)
http://www.frbsf.org/publications/economics/letter/2011/el2011-11.html
> And insured is probably the wrong word... I meant more
> like whatever "full faith and credit" is supposed to mean.
You might be confusing the Fed with the Treasury here. The Fed doesn't really have anything to do with the "full faith and credit" business of cash and debt of the US Government. To be sure, the Fed is in new territory, because they typically use the cash they get from member banks to buy and hold US treasuries; the interest earned goes to fund operations, and the rest gets paid to the Treasury. When they started buying Other Stuff[*] in the last few years, there became a very real possibility that they would incur a loss. So far the opposite has been true ...
> I thought you can't really conduct QE if you don't have notes
> backed by that clause and a whopper of an economy, right?
QE is basically the process by which the FRB buys assets in order to free up capital in banks who were holding whatever it was that they bought. You certainly can't do that without creating the money used to purchase the assets, which a central bank can typically do, but the money directly increases the reserve balances of the member banks. The real (disputed!) hope of QE is that by reducing the pressure of under-performing assets on the member banks' balance sheets, new productive lending can take place; the second hope is that the value of the assets purchased doesn't go down. The only real possibility of that has been with the Maiden Lane vehicles; the Agency Debt (along with Treasuries) of course are insured by the government now.
I think the big misunderstanding you're having is that QE is about *purchases of assets* and not *loans* ...
/jordan
[*] The biggest recent chunk has been Agency Debt (Fannie/Freddie, etc.), about $850B ... but this has been implicitly guaranteed by the government; the Maiden Lane portfolios (AIG, Bear Sterns, mostly) are far smaller: about $30B these days, out of about a $3T portfolio.