In a move against what he called “the ethics of payday lending” in higher education, Secretary of Education Arne Duncan announced Monday that the Education Department would forgive the federal loans of tens of thousands of students who attended Corinthian Colleges, a for-profit college company that closed and filed for bankruptcy last month, amid widespread charges of fraud.

Mr. Duncan also said the department planned to develop a process to allow any student — whether from Corinthian or elsewhere — to be forgiven their loans if they had been defrauded by their colleges.

A special master would be appointed within three weeks, department officials said, to create procedures to apply for relief that are “durable, not just for Corinthian but beyond.”

Taxpayers could pay a huge price for forgiving so many federal loans; the government has never before opened debt relief to such a potentially large pool of students. The department estimated that if all 350,000 Corinthian students over the last five years applied for and received the debt relief, that cost alone could be as much as $3.5 billion.