President Biden’s new “parole” program for illegal immigrant spouses of U.S. citizens will apply even to those who are defying court-issued deportation orders, according to the guidelines the Department of Homeland Security published Friday.

The program is slated to start on Monday.

Officials expect the program to cover 500,000 illegal immigrants who say they have been in the U.S. for at least a decade and who have married an American citizen. As many as 50,000 illegal immigrant children of migrant spouses are also expected to be eligible.

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According to the new guidelines, the program applies to people facing deportation hearings or who have already been ordered removed but are fugitives.

“If you are in removal proceedings or have an order of removal, you may still qualify for parole,” the guidelines said.

Some experts say that makes the program “amnesty” since it can postpone or cancel a looming deportation.

Immigrant rights groups had been anxiously awaiting the new guidance, hoping to get a quick start to filing applications next week. Some organizations have sign-up clinics planned.

U.S. Citizenship and Immigration Services said applications must be filed online. The agency is creating an all-virtual division to handle the cases, though the hiring process is moving slowly.

Much about the program remains murky, including the cost of applying and what crimes will be overlooked.

The guidelines say migrants with a “disqualifying criminal history” are ineligible, but it doesn’t say what is disqualifying.

That’s usually part of an official regulatory filing published in the Federal Register, but no such filing had been made as of early Friday afternoon, nearly two months after Mr. Biden announced the program and one business day before it starts accepting its first applications.

Rosemary Jenks, policy director at the Immigration Accountability Project, said the program is being hurried to beat the possible election of former President Donald Trump.

“The big time crunch is that they want to get as many people into this program to create a reliance interest before January,” Ms. Jenks said.

The reliance interest is a reference to a Supreme Court ruling on a previous deportation amnesty for illegal immigrant “Dreamers.” The justices, in a 2020 ruling, shot down a Trump administration attempt to shutter the program, arguing the migrants already in it had a reliance interest in continuing it.

Ms. Jenks also predicted the program would be subject to serious fraud. She said she expects migrants to create and backdate sham marriages or find ways to fake 10 years’ presence in the U.S.

The program relies on the homeland security secretary’s power of parole. That’s supposed to be a case-by-case grant of leniency for someone without a legal right to be in the U.S., and it’s supposed to be exercised only when there’s an “urgent” humanitarian need or “significant” public benefit.

The guidance welcomes migrants to make their case for how they qualify for one of those conditions.

To prove they’ve been here 10 years, applicants can use tax or school records, utility bills, medical records or financial records such as money transfers. Attestations by “organizations” are also allowed as proof.

Parole allows otherwise illegal immigrants to remain in the U.S. and obtain work permits, Social Security numbers and some taxpayer benefits.

Administration officials say that illegal immigrant spouses of U.S. citizens already have a path to citizenship but would normally have to return home to get a visa before converting to legal status. The new parole program allows them to skip going home.

“Noncitizen spouses and stepchildren who are granted parole in place through this process and who meet certain additional eligibility requirements may apply for lawful permanent residence based on their relationship to their U.S. citizen spouse or stepparent without being required to leave the United States,” the agency said.