Sometimes they have an egg on the way already, so an injured/sick hen will lay that egg.
If you can post some photos of her injuries, I will try to help you with her if you'd like.
The wounds would need to be flushed out really well. Since they are on the head/eyes, the use saline, that...
Do you have any updated photos of her?
It's very hard to know - depending on the damage, I would probably put her down. That's my first reaction to you initial photo.
I'm so sorry!
The poor thing:hugs
What are you wanting to do. Put her down or try to help?
If you want to help, we will try to help you, but with that damage if she survives for a few days, she's got a long road ahead of her and you will need to give her a lot of extra care, bringing her...
So you have the cage traps?
I've always used cheap stinky canned cat food, possum and raccoon both seem to like that here.
Placement of cage may need to be adjusted, if they are hanging out around that tree, maybe put the cage there?
Since they are going up that tree, if you have a safe clear...
Well it's sneaky!
Since you found the carcass in a tree, I would lean toward Bobcat, but....you have something that got the rest while you were moving around outside - Fox or Coyote.
My thoughts is you are dealing with more than one - a kill can bring in other predators.
Chickens just attract...
I don't know if a possum would climb a tree with something to eat, all the ones I have ever seen usually eat what they find in place.
It's possible the critter that killed them took part of the carcass up the tree or you may have more than one thing coming around.
If you can take photos of...
Oh dear! Do you have a secure coop for nighttime?
You may want to set some type of traps to see if you catch anything, but it would be good if you knew what was coming around - do you have a game camera?