Actually, since proof of vaccination is only required for immigration visas and not visitor, business or student visas this will keep happening.
As long as we are allowing unvaccinated people to travel legally and freely in and out of the country, we will have outbreaks.
They already know this latest outbreak originated in the Ukraine where Hasidic pilgrims picked it up and took it back to Israel and American visitors to Israel brought it back to the orthodox communities in New York.
The Washington outbreak is also the Ukrainian strain and patient zero was a visiting child that infected his peers at a church. While they aren’t identifying the church, the smart money says Eastern Orthodox.
While it’s not illegal immigration per se that is the problem in this instance, it is part and parcel of the stupid border policies that congress refuses to fix.
Decades ago, we had to have vaccines against several diseases before being allowed to travel in foreign countries. Do they/we not require that today? Stupid policy if not.