are you looking to insure the hens or the structure itself? if you're paying rent on an informal basis, then sounds like any liability would be on your friend (and their insurance). i'm not a licensed agent though - i just work with a lot of them.
I think it would be hard to insure against theft specifically because how would you prove it was (human) theft vs a predator? perhaps just upgrading the locks on the hen house would provide some peace of mind if you're really worried.
but you might see if you can find an insurance agency that specializes in farm/agriculture insurance and pick their brain about it.