WASHINGTON (Reuters) - Mortgage finance companies Fannie Mae (NYSE:FRE - news) have new programs to help troubled subprime borrowers avoid foreclosure, the companies' chiefs will say Tuesday, according to prepared testimony for a congressional hearing. Daniel Mudd, Fannie's Chief Executive Officer, will unveil a new effort called "HomeStay" when he testifies Tuesday before a congressional panel to discuss the subprime lending crisis, according to text of his prepared remarks obtained by Reuters. The program will offer troubled borrowers "a range of workout solutions," looser credit requirements and ways to shed subprime mortgages before payments spike, according to prepared testimony to...