CHICAGO -- Education Secretary Arne Duncan said Tuesday that he remains open to having his agency cancel the federal student loans of some borrowers who attended Corinthian Colleges.

“Everything’s on the table,” Duncan said during remarks at the Education Writers Association conference here.

Duncan said that the Education Department was working to figure out “a fair and impartial” way to handle the more than 250 claims filed by former Corinthian students formally asking to have their debt canceled.

Consumer advocates, student activists, some Senate Democrats and nine state attorneys general have asked the department to make it easier for federal loan borrowers to apply for debt relief.

They have pointed to a mostly dormant provision of federal law that allows borrowers to assert misconduct by a college as a reason why they shouldn’t be legally responsible for repaying their loans.

Over the past 15 years “we’ve had, like, four of these cases,” Duncan said Tuesday. “So we don’t have a lot of practice on this. The rules aren’t very clear.”

“There are certain things in the law that students would have to prove” in order to have their loans canceled, he added.

Duncan also framed the Corinthian debt forgiveness issue in the larger context of the administration’s crackdown on for-profit colleges. The department last week fined Corinthian-owned Heald College $30 million over allegations it misrepresented job placement rates.

“We’re trying to make up for some real wrongs at the back end,” Duncan said.

Separately, state regulators in California announced this week that they have ordered Corinthian’s campuses operating under the Everest and WyoTech brands to stop enrolling new students. The emergency action, which takes effect Thursday, means that only a handful of remaining Corinthian-owned campuses, such as its Rochester, N.Y., and Phoenix locations, are allowed to seek new students.