Seems like part of the answer here could be to change the college application process to in-person interviews, group discussions, and in-person essays and assignments. A super time-consuming process and logistically much harder to do, but seems worth it to find the students who want to be there.

Paging Congress

And more are likely to try to migrate

We're watching an almost exact replay of the initial Abrego-Garcia crisis, where Trump is behaving like an honest-to-god dictator and Democrats are tiptoeing around the issue because they're afraid to be seen defending immigrants, cities, whatever. They only see risks, not opportunities.