You get the cat, but it’s a traveller so it can’t do some things.
Travellers can’t:
do jobs
raise a family
basically the stuff that requires being in the active village
But travellers still can:
be renamed/edited
have relationships
send letters
dress up
etc. Your travelling catpacity is 4x your active catpacity. Travellers have to stay travelling for a few days when you send them travelling. There’s a view travellers button in your village cats page.
Essentially it’s a way to free up working cat slots while keeping your cats.