I don't think the airlines handle this but CBP, they will most likely find the first available flight to the person's country of origin and put them on. The US governments pays. As far as luggage, once a person is placed in secondary screening or detention, the luggage are already out on the carrousel and airline representatives would probably bring them to the detained passengers.
United has issued a statement saying anyone carrying a visa or refugee status from any of the 7 countries won't be allowed to board. They are allowing US legal residents to board however.