Hen with a wound.

[pharrison4659]

Glad she's doing better, hope she makes a full recovery.
Rats will travel a good distance to get food, so if neighbors have them then it's possible.
Feed usually gets spilled by the birds no matter how hard you try to keep it cleaned up, and that is a big attractant for rodents. They particularly like to live in brush piles or debris piles, or in spaces under buildings.
If you can set a trap, I would do that, see if you catch anything and then you will know for sure. Or alternately set up a game camera in the coop, see if anything is coming in at night.

Thanks so much for bringing this to my attention!