Assuming it is store country that is checked: Simply VPN-ing doesn't change that. Instead you have to make a purchase in the new place with "a payment method from the region you have moved to". From experience this locks your account to the new region for 3 months. What would be interesting to know is if you can be in a family and then change regions afterwards without getting auto-kicked.
Needless to say, my experiments ended at trying to see if they have any kinds of restrictions in place (unlike for the original family share) and I don't wanna buy a throwaway game and lock an account into a different region for 3 months just for shits and giggles.
I'm pretty sure this was already the case in some games before, depending on the netcode of the game.
The old FAQ said:
If it's a game with VAC it probably always worked as described above, but for example: People in Fall Guys did use this trick to avoid getting banned for cheating until they turned off Family Share for Fall Guys shortly after release.