My brother and sil had a cat that was only theirs when they still lived with us. She wasn’t allowed out of their room to socialise with the other cats in the house. When they moved out, they left her with us because my sil wanted a friendlier cat.
No problem for us, we already had 2 cats and a dog, one more isn’t a big deal. That little cat is the sweetest, funniest thing. She always has a lot to say. If you touch her she meows. If you talk to her she’ll meow at you. She doesn’t cuddle, but she loves being petted and will purr up a storm. She also had no problem whatsoever adjusting to having free reign of the house and the other animals.