State attorneys general are descending on Washington again this week for negotiations with federal regulators and the nation’s largest mortgage servicers over the purpose of a multibillion-dollar fund aimed at helping troubled borrowers.

The idea behind the yet-to-be-created fund, the size of which remains in flux but could eclipse $20 billion, is to punish the servicers for their shoddy foreclosure practices, which came to light in the fall, and to put that money toward keeping struggling homeowners in their homes.