I lost two early on from something digging under the fence but haven't had any trouble since then. I couldn't afford to build an enclosed coop at the time. I'm hoping this summer I can update it a little.
Do you have a dog? If I did I would setup his doghouse under that eve. Otherwise cheapest option would be to fence in entire area to make a very large coop. Lower four feet I would reinforce with another type of fencing to at east slow dogs. Make so you have a live-trap out at all times for raccoons and oppossums.

