If a family member gets banned for cheating while playing your copy of a game, you will also be banned in that game.
This sucks.
On the other hand, Rust had a cheater issue at some point because they only checked the account ID when banning in EAC. Cheaters leveraged this by purchasing the game in a master account, and using secondary accounts tied with Steam Family Sharing to play. From what I can see they disabled Family sharing altogether.
Secondary account banned? No problem. Log out, share with another account, rinse and repeat.