The federal government will make it easier for more students who attended the now-defunct Corinthian Colleges to get rid of their federal loans, officials announced Monday, as part of a new plan that could cost as much as $3.6 billion.

Corinthian Colleges was one of the largest chains of for-profit colleges when it nearly collapsed last year and became a symbol of fraud in the world of higher education and student loans. According to investigators, Corinthian schools charged exorbitant fees, lied about job prospects for their graduates and, in some cases, encouraged students to lie about their circumstances to get more federal aid.

Some veterans advocates have accused the for-profit education industry of aggressively targeting veterans because of their federal GI Bill money. Critics say the schools are too expensive and a waste of money not just for students, but for taxpayers who fund the GI Bill and other loan and grant dollars used by a large chunk of students to help pay to attend for-profit colleges.

In a plan orchestrated by the Education Department, some of the Corinthian schools closed while others were sold before the chain filed for bankruptcy protection this spring. The biggest question has been what should happen to the debt incurred by students whose schools were sold. The law already provides for debt relief for students of schools that close, so long as they apply within 120 days.

The latest plan expands debt relief to students who attended a now-closed school as far back as a year ago. And it streamlines the process for students whose schools were sold but believe they were victims of fraud. The Education Department will soon appoint a "special master" to oversee much of the program, and support students at other for-profit schools who feel they've been victimized.

"We will make this process as easy as possible for them, including by considering claims in groups wherever possible, and hold institutions accountable," Education Secretary Arne Duncan said in a statement.

Duncan told reporters during a phone call Monday that the department has no way of knowing how many students will come forward and ask for help.

About $3.6 billion in federal loans has been given to these students since 2010, the department said. That potentially puts the taxpayer on the hook for that amount, although officials say it's unlikely that every loan will qualify for relief.

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Still, the amount is likely to be significant. Officials estimate that some 40,000 borrowers at the Heald College — one of Corinthian's subsidiaries — alone took on more than $540 million in loans that potentially qualify for debt relief. The final amount could climb significantly when looking across all Corinthian Schools, which include Everest and WyoTech.

Dianne Torres, 24, who lives outside of Los Angeles in Whittier, California, said she has been angry that she hasn't found a job since completing a 10-month medical assistant program at Everest College shortly before the school closed this spring. But, she said, she's not sure she wants to apply to the debt relief program just yet because that would require her to give up her diploma.

"I dedicated 10 months of my life doing it because I wanted to get a better job for my kids. So it's really hard for me to go here, then have to give the diploma back," she said.

About 100 current and former students have already refused to pay back their loans. Organized by the Debt Collective, each member of the "Corinthian 100" has amassed tens of thousands — even $100,000 or more — in federal and private loans in areas of study such as nursing and criminal justice.

The former students argue that the department should have done a better job regulating the schools and informing students that they were under investigation.

In a blog post Monday, the Debt Collective said the Education Department plan didn't go far enough. They said the plan would put in place "a bureaucratically tortured process designed to provide relief only to those who hear about it and can figure out how to navigate unnecessary red tape."

Rep. Elijah Cummings, D-Md., and Sen. Barbara Boxer, D-Calif., praised the move by the administration, even as it left glaring questions about whether the government could have done more to protect students in the first place.

"It is our responsibility to hold servicers and colleges accountable to prevent future students from having to endure anything like this debacle ever again," Cummings said.

California Attorney General Kamala Harris said the debt relief should give students hope. Harris had filed a 2013 complaint that alleged Corinthian schools targeted low-income residents via the Internet and telemarketing. She was one of several attorneys general who pressed the Education Department to forgive the debt.

"Corinthian profited by preying on the educational dreams of vulnerable people and then left them under a mountain of debt," she said in a statement.

Former officials at Corinthian Colleges couldn't be reached immediately for comment. A former lawyer for the school said he no longer represents the chain of colleges since it went bankrupt.

Most of the company's assets have been sold and its stock is worthless.