Can the FBI just arrest Greg Abbot?

[LeftInTX]

85. The immigrants are processed at the border and are given a hearing date.

Then, they are on their own.
It is the immigrant's responsibility to show up at their hearing. Fortunately, agencies in NY and DC have been able to reschedule hearings to their new location.

But once they are processed and given their hearing, they are on their own.

There are a few things that they are not allowed to do and if they are caught, they can be deported. But other than that, they are free to live with whomever, shop wherever and live wherever in the US. They are not allowed to work, but many end up with cash paying odd jobs. (Sometimes this leads to their exploitation)

DHS and immigration really don't keep tabs on them. They are expected to show up at their hearings. If they don't, they can be subject to deportation.