I am agreeing with hawk or owl. I know an owl will drag its prey under something as I have had this happen. I have never seen a hawk do that but I don't rule it out. The only other slight possibility would be a weasel, but probably not. I have fruit tree netting (cheap) across the tops of my pens and it does keep predators out. If a predator does manage to drop through the netting they will not get out. What you do with the predator is your business.