We all know that 「ある」is to be used with inanimate objects and 「いる」with animate, living things. However, almost all examples of usage that I've seen thus far is in the context of something or someone being there. There is a cat there. There is a man there.
What happens when it comes to listing the ownership of items? If I were to say that I own a cat, does the rule to use「いる」still apply?
（I get that usually one would use かっています here, but this just for the sake of example)
In this case, the former sounds wrong (at least to me), even though it follows the rule. The latter vice versa.
In another example, what if I don't physically own something, but rather have someone?
Both the above sound correct to me, even though in both example, the subject is living and 「いる」should be used.
Can someone clarify?