Thousands of undocumented immigrants in the North Bay possibly could benefit from a new federal policy that would ease rules on seeking permanent residency that now force the separation of some families.

The final rule, initially proposed a year ago, was announced Wednesday by the Obama administration and would allow immediate relatives of U.S. citizens to apply -- without leaving the country -- for a waiver from the 10-year ban for unlawful presence.

Currently, an undocumented immigrant must leave the country and request the waiver at a specific U.S. consular office in the immigrant's country.

For Mexican immigrants who have entered the country illegally or overstayed their visas, that office is in the crime-ridden border city of Ciudad Juarez.

If the waiver is rejected, the immigrant is barred from entering the United States for three years if they were in the country illegally for 180 days or more or 10 years if they were in the country illegally for a year or more.

"This is a huge, huge benefit. It reduces or eliminates the risk that they'll be separated for 10 years from their family," said Christopher Kerosky, a partner with the Bay Area law firm of Kerosky Purves & Bogue, which has offices in Santa Rosa, San Francisco and Walnut Creek.

"We're talking about probably thousands of people in the greater North Bay, or at least many hundreds," said Kerosky, whose firm specializes in immigration law.

Federal officials estimate the change could affect as many as 1 million of the estimated 11 million illegal immigrants in the U.S., the Los Angeles Times reported.

The waiver is granted only in cases where the U.S. citizen spouse or parent can prove that separation from the undocumented relative would cause extreme hardship on the family.

The government did not not define "extreme hardship" despite requests from legal aid organizations to do so. Citizenship and Immigration Services "looks at the totality of the applicant's circumstances and any supporting evidence," according to the final rule published Wednesday in the Federal Register.

The rule was proposed in January 2012. After taking public comment on it, Citizenship and Immigration Services, an agency of the Department of Homeland Security, announced the final rule, which takes effect March 4.

Immigrants still must leave the country to obtain visas but now will do so knowing they have been granted a waiver. Many immigrants have not pursued a waiver out of fear they would be rejected and stuck outside of the U.S.

A Homeland Security spokeswoman, who asked not to be named, said the federal government does not intend to pursue deportation proceedings against those who have been denied a waiver or have withdrawn their application.

Immigrants and their families may begin filing for waivers on or after March 4.

"For the first time, we got a hard date for when people could start to apply," said Santa Rosa immigration attorney Richard Coshnear. "Hopefully, it will ease the pain of separation for a number of families."

But Coshnear cautioned "people still need to prove that their spouse will suffer hardship. It's still a difficult thing to get."

The new policy is the latest move by the Obama administration to use its executive powers to revise immigration procedures without Congress passing a law.

In August, the administration launched a program to halt the deportation of young people brought to the U.S. unlawfully as children.