Prob not rabid tho. Rabbies kills in days Utube it u will see its pretty distinctive.
I guess u didnt read the part about being in long island... NY aint a fly over state where u shoot shovel. U shoot a gun in LI your going to jail. Simple.
Use a double fencing system, its best. That's why prisons, military bases everywhere that needs security uses two fences.
Alternatively if u dont want to spend a lot of $$ you could just go buy a trap set it next to your hen house put some bait in there and just continually have a trap that will be an easier target then the hens... now what to do with the animal when you have a trapped that's entirely up to you.
You can also put a mets jersey in the cage once they see the hens are mets fans they will realize its not even worth there time!!!