Nope, it defaults to an informal tenancy if they’ve been living there long enough (usually something like 3 months), and this includes the time when they were under 18. So if a child grows up in the home, they automatically become a tenant at 18. This is also regardless of whether they actually pay rent.
You don’t need a written contract for there to be a contract in place.
OP asked what their rights were, so that was the focus of my reply. You’re right though, and I’ve said as much in my main comment, it’s better to avoid the situation entirely than to stick a finger up and try to assert your rights.