They become stateless and generally get stuck in a port afaik

Assuming they are American, they can only give up citizenship at a foreign embassy, meaning that they would already be in another country.

Texas, they want to separate anyway

you can just expel them from the country, then the only place they can go to is the un

In Shemima Begum's case, no where. She's stuck.

They would need to find an unclaimed island, I guess. Or isn't Antartica's status that it doesn't belong to any country? We could suggest that.