Unlike what Texas and Florida would have you believe with their migrant busses, seeking asylum is a legal method to get into the US.

The process is basically that someone shows up at the border, claims asylum, and they’re asked if they believe they’re persecuted (not are, that they believe they are) for any of several reasons.

Then they can stay in the US legally and work for up to a year, with travel restrictions, while waiting for a court case to determine if it’s a valid asylum claim. If it is, they continue to stay. If it isn’t, they’re deported.