Exactly, it's the very reason the banks use FnF to begin with--to eliminate the debt on their books.
This description of FnF's role is classic:
"How they do this is simple: After a bank decides to make a mortgage loan, Fannie Mae buys the loan from that bank. This is what actually makes it possible for middle-class people to afford homes — without Fannie, retail banks would have to hold the mortgages they’ve written on their books, so they’d be extremely vulnerable to relatively small, local shocks to the economy. Under these conditions, many banks would decide simply to avoid the mortgage market altogether, making it incredibly hard for middle-class people to get approved for a loan. So Fannie’s role here is 100% good stuff; the problems in the housing market started when privately held companies got heavily into this business and decided there was money to be made by doing away with “lending standards” and letting Goldman Sachs slice up the resulting destined-to-fail loans, mash all the bits together, and sell the resulting shit sandwiches to everyone’s pension funds."
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