Really, it just depends on the specific animal.
We have three cats, four now that my sons is staying with us. They have a scratching post and wreck that, but don't tear up anything else. We use covered litter boxes, so they can't miss. Once in a great while one of them does their duty somewhere else, but its almost always because we've made them mad somehow or another.
My sister's cats, on the other hand, have totally wrecked her couch. No damage to her house, but he couch is toast.
We have a small dog, a cairn terrier. No problem with tearing up anything inside, but he's a digging fiend outside. He has a big run, but there's always something more interesting outside. So, for about two feet inside the fence, the ground is covered with 2x4 fencing to keep him from doing a great escape.
Some friends used to have great danes in their rental house. One day they got to chewing and pulling on the hose, which was hooked up to the bib. You see where this is going, right? Anyway, they pulled the pipes out of the wall and flooded the place. Good thing this was Houston where there are no basements or they would have had an indoor swimming pool.
For a random animal you know nothing about, its a total crap shoot.