Alums of a disgraced for-profit college chain have spent years trying to cancel their federal student loans. For three years in federal court, the Obama Department of Education told them to keep on paying. Improbably, the Trump administration is poised to say different.

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Under a preliminary accord, the federal government would invite tens of thousands of former students, who more than 20 years ago attended beauty and secretarial schools owned by defunct Wilfred American Education Corp., to petition the Education Department to cancel their unpaid debt and receive refunds on past payments, according to four people familiar with the case, who spoke on condition of anonymity because they were discussing confidential settlement negotiations. The applications are almost certain to be approved, these people said, and the government would foot the bill.