By Les Christie @CNNMoney February 10, 2012: 11:02 AM ET

NEW YORK (CNNMoney) -- In an effort to cut their losses, banks are paying some struggling homeowners as much as $35,000 to sell their homes before they end up in foreclosure.

The deals are aimed at incentivizing homeowners who owe more on their home than it is worth and who are seriously delinquent on their payments to sell their homes in a short sale.

The bank offered Angelique Pierce $25,000 to short sell her home. The listing price: $95,000.

In short sales, homes are sold for less than what is owed and the bank forgives the excess debt. Banks have been reluctant to approve such deals in the past -- since they take a loss on the home -- but in certain cases, it's become a much better proposition than letting the homeowner fall into foreclosure.

This new approach by the banks has startled plenty of homeowners, according to Elizabeth Weintraub, a Sacramento-area real estate agent who specializes in short sales.

"Initially, the homeowners are skeptical," she said. "The bank may have already turned down their request for a modification. Then, one day, they call and say, 'Let us give you some cash.'"

When Chase Mortgage (JPM, Fortune 500) told Angelique Pierce, that she would receive a check for $25,000 if she sold her house, she couldn't believe it.

"I got the offer in the mail," said the Rancho Cordova, Calif. resident. "I called my bank to ask if it was real."

After Pierce became disabled a few years ago and had to stop working work, she fell behind on payments on both her first and second mortgages, valued at $250,000 and $50,000, respectively.

Now, she's trying to sell her three-bedroom ranch for just $95,000 -- almost half of the $179,000 she paid for the place in late 2002.