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You'd be surprised at type of things that try to get at birds. Typically birds found in pens without heads are from an owl. At night an owl will swoop down to get the birds to flush, the owl then grabs the head, unable to pull the bird thru the net, both the head and body fall to the ground. Generally this happens around the perimeter because birds hiding in the cover are less likely to flush.

I have seen raccoons do that type of damage. They can actually read through nd grab the birds neck and will try and pull them through the fence.