The Trump administration has drafted a new rule that would severely limit the ability of people crossing the U.S.-Mexico border to seek asylum in the United States, according to a report by Vox.

Currently, migrants who cross the border without papers between official ports of entry can apply for asylum, even if they are prosecuted for illegal entry. The rule drafted by the Justice Department, which has yet to be released and opened up for public comment, would eliminate that right. If the rule is made final, anyone convicted of entering the U.S. illegally — either for the first time or repeatedly — would be completely ineligible for asylum, according to Vox.

With President Trump’s “zero tolerance” policy of prosecuting every single person crossing the border, and with the U.S. government turning away asylum-seekers who present themselves legally at ports of entry, this would effectively shut the door on all asylum claims from the thousands of people currently fleeing Mexico and Central America.

The reported restriction comes just a few weeks after Attorney General Jeff Sessions announced that asylum will no longer be granted to migrants fleeing gang violence and domestic violence, and would constitute the most severe restriction in decades on the right to seek asylum in the U.S.