Not likely enough surface area for cyanoacrylate to do its magic, though one could try to glue the key pieces together and hope it holds long enough for a partial pull. Likely to just glue the broken piece in there by accident.
Hot glue is gooey and will grab the broken part.
Our Skogkatt ate teen rabbits regularly. She would bring them into the house so we gave her a "murder mat" that was for that purpose (smart cat, didn't need training and immediately started using it).
She had a hip problem so didn't bother with birds, and we let her roam the "farm". The rabbits she mostly ate at home were nearly full grown eastern cottontails.
One day she brought in and ate two smaller 5-week old or so teens, side by side. Always ate everything but the kidneys and maybe a foot or nose. She also ate the giant dock rats that show up sometimes around the chickens.
Scary little ambush predator. Owls are just as impressive.
Barn Owls and lots of other big claw birds around here thrive on the naturalized cottontails. But they are mostly part of the ecology that eats smaller things like voles or snakes.