More than 4 million American homeowners, or 9 percent of borrowers with a mortgage, were either behind on their payments or in foreclosure at the end of June, according to the most recent data from the Mortgage Bankers Association. To qualify, borrowers would have to be at least three months behind on their home loans and would have to owe 90 percent or more than the home is worth. Investors who do not occupy their homes would be excluded, as would borrowers who have filed for bankruptcy. Qualified borrowers would get help in several ways: The interest rate would be reduced so that they would not pay more than 38 percent of their gross income on housing expenses. Another option is for loans to be extended to 40 years from 30, and for some of the principal to be deferred, interest-free.