Canada is facing pressure to scrap an agreement that prohibits anyone who is entering the country by way of the United States from applying for refugee status.

The Safe Third Country Agreement, established in the aftermath of 9/11, is taking on new implications in the wake of President Donald Trump’s immigration crackdown, with advocates, lawyers and border guards saying it endangers migrants by pushing them to cross the border illegally.

The number of people making clandestine crossings to Canada has already shot up in recent years, and that trend is expected to increase following a sweeping executive order from the Oval Office that targets Muslim-majority countries.

On Friday, the president indefinitely suspended refugee admissions from Syria; banned admissions from all countries for three months, while the government decides which countries to allow; and prohibited entry — immigrant and nonimmigrant — from Iraq, Syria, Iran, Sudan, Libya, Somalia, and Yemen for 90 days.

“That’s going to put more pressure at the border with this unfortunate Safe Third Country agreement, which forces most people to cross illegally,” said Janet Dench of the Canadian Council for Refugees. “That’s bad for them but good for smugglers because they take advantage of people in this situation.”

The agreement, based on the notion that the United States and Canada are both safe countries for refugees, says claimants have to apply for refugee protection in the first country they arrive, with a few exceptions. But refugees have been taking their chances, entering the country through back roads and evading the Royal Canadian Mounted Police. Unlike the United States, Canada doesn’t have a dedicated border patrol. Some have drowned while swimming across the Niagara River. Others have died traversing railway bridges.

Those who do make it to the other side can have their claims heard but they too pay a price. Like two Ghanaian men, who trudged for an entire night through waist-deep snow to cross the Emerson, Manitoba border over the holidays and will likely lose fingers to frostbite.

In Toronto, a doctor also treated nine cases of frostbite in refugees, who report being smuggled across the US-Canada border in trucks and left waiting at a drop-off point for someone else to come pick them up.

“Loss of life and limb is what’s happening as a result of this agreement. Get rid of it, let people make a refugee claim,” said Bashir Khan, an Winnipeg-based lawyer representing the two Ghanaian men. “Surely our system can have faith in our independent refugee protection system, which would weed out those cases that need protection from those that are not.”

Jean-Pierre Fortin, president of Canada’s Customs and Immigration Union, said at current staffing levels, frontline border services officers don’t have the ability to face any increase in demand right now, and that demand is almost certain to increase with Trump’s order.

According to the Canadian Border Services Agency, 430 refugees, mostly from Somalia, crossed the border in Manitoba illegally between April and early December of last year, up from 82 from the same time in 2013. The number has also gone up dramatically in Quebec, with 823 caught crossing between April and end of November last year, compared to 166 two years prior.

“[The agreement] is encouraging people who want to come into our country to cross illegally,” said Fortin. “That’s a huge problem, and it exposes all the weaknesses of the border where these folks can cross.”

Efrat Arbel, a UBC law professor who is studying the Safe Third Country Agreement, says if Canada takes its refugee protection obligations seriously, “then that comes with a mandate to re-evaluate whether we can adequately consider the United States to be a safe country for refugees, and I think we cannot.”

“And the logical corollary of that would be that we have to scrap the Safe Third Country Agreement,” she said.

Arbel says irrespective of the order, in some ways the American asylum system already falls below international standards of refugee protection, whether it’s its higher burdens of proof, procedural barriers, or abuses in its immigration detention system.

But Trump’s actions to restrict admissions to Syrian refugees, as the world faces “the greatest humanitarian crisis since World War Two” is contrary to every basic principle of refugee protection, said Arbel.