Facing heavy losses and a crackdown by government agencies, Corinthian Colleges, one of the largest for-profit operators of trade schools and colleges, will largely cease operating under an agreement with the federal Education Department.

Corinthian, which has about 72,000 students, will make arrangements in the next six months to sell almost 100 schools in the United States and Canada, and it will close a dozen others, the company said in a statement released late Thursday. That appears to cover all of Corinthian’s schools, but the company left unclear whether it would continue to exist in some form or retain any of its current programs.

The agreement “provides a blueprint for allowing most of our campuses to continue serving their students and communities under new ownership,” said Jack D. Massimino, chairman and chief executive of the company.

But the plan faces a major hurdle: finding buyers. College enrollment has been declining, particularly in the for-profit sector, and several other companies are having financial and regulatory troubles of their own.