How to set fog to not be around an object?

I wanted to create a place, where you could only see the objects that were yours, except I ran into a problem. The player's stuff is large scale, and the Dynamic lighting won't extend far enough out, and when I"m a certain distance away from the object while I can still see it, the dynamic lighting disappears. I figured I could use fog, but that's based on the Camera and I would need to set it to not be around an object, does anybody know if it's possible to make fog not go around an object?