In fact there's an article in the NY Times today, see below, but as others have pointed out, most banks aren't capable of doing it for a number of reasons
Fannie Mae Allows Renters to Stay
In a move that provides relief to thousands of renters who face eviction but draws the federal government even deeper into the housing market, the loan giant Fannie Mae said Sunday that it would sign new leases with renters living in foreclosed properties owned by the company.
It is the first nationwide effort to provide widespread relief to renters ensnared by the unfolding mortgage crisis, and it will effectively transform Fannie Mae — a government-controlled mortgage finance company — into a national landlord. It may also increase pressure on private lenders to establish similar programs and on lawmakers to pass renter relief.
“There are renters all around the country who have been holding up their end of the bargain and paying their rent faithfully, but the landlord got into trouble, and so the renter is now unfairly facing eviction,” said John Taylor, president of the National Community Reinvestment Coalition, a consumer advocacy group. “It’s really good news that Fannie Mae is doing this. Now the question is whether private sector will follow suit.”
In recent months, skyrocketing foreclosure rates have exposed as many as 70,000 renters to evictions, even though many never missed rent payments, according to analysts who track housing data. In many cities and states, renters can be evicted after their home goes into foreclosure, regardless of how long their lease stretches into the future.
http://www.nytimes.com/2008/12/15/business/15evict.html?ref=business