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Thousands of people who lost their homes to foreclosure are now eligible to buy back those properties at current market value if their loans were backed by Fannie Mae or Freddie Mac.

Fannie and Freddie previously required borrowers who wanted to repurchase their homes to buy them for whatever amount they owed on the mortgage – even if that amount exceeded the fair market value of the home.

That policy was scrapped by the Federal Housing Finance Agency, which oversees Fannie and Freddie. “This is a targeted but important policy change that should help reduce property vacancies and stabilize home values and neighborhoods,” Melvin L. Watt, FHFA director, said in a statement.

The change affects 121,000 foreclosed homes owned by Fannie and Freddie as of Nov. 25. But it’s unclear how many people will be in a position to take advantage of it. Some former homeowners may have moved on, and a repurchase may not be practical for them. Many may not qualify for financing.

Some of the financing challenges have to do with Fannie and Freddie’s own rules, which require borrowers to wait at least three years after a foreclosure before they can qualify for a mortgage. That rule will not change, which means most of the people interested in a buy back would have to look for alternative financing, such as loans provided by non-profits such as Boston Community Capital.

BCC buys homes in Massachusetts, Maryland, Rhode Island and Illinois that are in foreclosure or close to it. It then resells or rents the homes to the former owners at a price that reflects the property’s current market value.

"I applaud the FHFA for taking this step and allowing homeowners to have the potential to remain in their homes," said Elyse Cherry, BCC's chief executive. "This has been a long time coming and it makes a lot of sense."

For years, Fannie and Freddie barred buy-back arrangements because they basically amount to a “principal reduction,” a form of mortgage relief that reduces the size of a troubled borrower’s mortgage. This type of relief has been a hot button issue ever since the housing market unraveled and home prices plunged. Millions of homeowners saw the equity in their homes get wiped out, and they could not sell or refinance their way out of trouble. Principal reductions are one of the most effective ways to ward off foreclosure in such cases.

The Obama administration had pressed for Fannie and Freddie to allow such debt reductions through the government’s main foreclosure prevention program, known as the Home Affordable Modification Program. In 2012, the Treasury Department even offered to pay Fannie and Freddie to participate.

But the FHFA, under Watt’s predecessor, feared that such relief would entice homeowners to intentionally default on mortgages in a bid to get cheaper loans. The agency also warned that such relief could be costly for taxpayers, who had already spent billions of dollars to bail out Fannie and Freddie in 2008.

Last week, when pushed at a Senate hearing to take a position on principal reduction, Watt said that this type of mortgage relief was not “off the table.” He said the issue was “perhaps the most difficult he has faced” as FHFA director.

But even before Tuesday’s announcement, there were signals that the agency was easing up on its position on buy-backs in particular.

After years of wrangling, Fannie recently allowed Jaime and Juana Coronel to buy back their Los Angeles area home at its fair market value after it slipped into foreclosure in 2010. The couple been living there for 20 years when Jaime Coronel’s landscaping work dried up during the recession and they fell behind on their mortgage payments. Fannie let them rent the property for a few years but tried to evict them when it wanted to sell the house.

The couple refused to budge and asked to buy back the home, a plight detailed in The Washington Post in July. Fannie eventually agreed, and the Coronels purchased the home for $280,000. The deal closed two weeks ago, according to the Alliance of Californians for Community Empowerment, which has been helping the couple.