I think it takes a lot of patience and understanding to have pets in the first place, but certainly to take on an animal with "issues".
The agency I work with is very careful to be honest about what we know about a particular animal. And they are that, animals. You'd be astounded by the number of people who act surprised when we ask questions about how they would deal with the cat scratching the furniture, or making occasional messes. It either never occurred to them, or they specifically request a cat that doesn't ever throw up or scratch anything. Um, if that's what you're looking for, you don't want a cat, at least not a live one. Go get a stuffed animal.
Cats scratch stuff, you have to clean their litter box daily, they meow, they shed fur. Dogs bark, chew, shed, and have to be taken out multiple times a day, and in many areas you have to pick up their waste (except some of our neighbors, who leave it in the grassy area between our side door and our car
). I mean, a pet is a joy (IMO), but also a chore.
My mom adopted a cat one year that showed up on her doorstep (not the first time that happened, either). He flinched every time you tried to pet him, and once inside with the other cats, there were fights all over the place as our one boy (he thought he was an alpha male, which was really more by default than anything else, and he was a big bully) did everything in his power to terrify and beat on the new and obviously previously abused cat. My mom almost gave him up, she was so worried. But she stuck it out.
It took years for the cat to stop flinching (less time than that for the other cat to finally leave him alone, thank God), but once he settled down, what a grateful and loving cat. He was constantly rubbing ever piece of furniture, and loved nothing more than to give head butts to his people. He had the strongest tail I've ever seen on a cat - when it would lash, it could actually hurt a bit if he hit you with it.
This boy (whom my mom named Ebenezer, but we all called Slinky because he of how he wound his body around everything) died as I was petting him from either a stroke or a brain aneurysm or something like that. Instead of a lifetime of abuse from where ever he came from, he ended up in a home where he was well loved, and he was happy.
I took this photo about a month before he died. He was a great cat.