In an effort to end the foreclosure crisis, the Obama administration has been trying to keep defaulting owners in their homes. Now it will take a new approach: paying some of them to leave. This latest program, which will allow owners to sell for less than they owe and will give them a little cash to speed them on their way, is one of the administration’s most aggressive attempts to grapple with a problem that has defied solutions. More than five million households are behind on their mortgages and risk foreclosure. The government’s $75bn mortgage modification plan has helped only a small slice of them. Consumer advocates, economists and even some banking industry representatives say much more needs to be done. For the administration, there is also the concern that millions of foreclosures could delay or even reverse the economy’s tentative recovery — the last thing it wants in an election year. Taking effect on April 5, the program could encourage hundreds of thousands of delinquent borrowers who have not been rescued by the loan modification program to shed their houses through a process known as a short sale, in which property is sold for less than the balance of the mortgage. Lenders will be compelled to accept that arrangement, forgiving the difference between the market price of the property and what they are owed. “We want to streamline and standardize the short sale process to make it much easier on the borrower and much easier on the lender,” said Seth Wheeler, a Treasury senior adviser.