US consulates, including the one in Barbados, offer Consular Outreach Visits for U.S. Citizen Services:
In order to better serve U.S. citizens living throughout the Eastern Caribbean, the U.S. Embassy in Barbados makes every effort to send a Consular Officer to countries in our Consular District approximately twice a year to offer certain American Citizen Services such as accepting applications for U.S. passports and Consular Reports of Birth Abroad, and provide notarial services.
I had a look through their events calendar and don’t see anything coming up for Guadeloupe, but it would be worth asking them. The US citizens in my family have used this service in our part of the world and it is definitely more convenient than travel to the consulate location.
If they manage to get to a port of entry, they should eventually be admitted, though it may not be a fun experience.
However the airline will almost certainly not let them board an international flight without valid passports, so what would happen on arrival is kind of moot.
Credit:stackoverflow.com‘