Each bird is different. All of my chickens and ducks are capable of flying over the 42" fence I have around their free range yard, but none of the chickens have gone over it, and only 4 of my ducks do it on occasion (to get to the kiddie pool I have outside the fence). Sometimes you will have a hen that will constantly fly over a fence, not matter how high. My guineas would regularly perch on the peak of the shed and garage, easily 20 feet from the ground. If you have a flyer, you may need to clip its wings. That said, I do have a roof over the small 15x15 run attached to the coop, so the birds can get fresh air anytime and not be in danger from predators. They only go to the free range area when I am home.
Our fence is only 3 feet. Our girls are constantly going over it. I haven't bothered to switch it to 4 foot, because I figured they could go over that, too. I haven't seen the need for a cover. They come back to go to bed. As for predators...now you've got me nervous. But the tree they sleep in is in the middle of their run, so they wouldn't have anywhere to sleep if I put nets up.
As others have said, they'll get over it if they want to. But it's not easy for them especially if you clip ONE wing and they'll get tired of it unless they have a really good reason. Our fencing is 4' and after the novelty wears off they stay inside. It helps if you're there to round them up before something else does. We have some large window screens that we prop up to form a funnel to the door to the coop and herd escapees into the funnel. Had to do it a few times with each new batch of chickens.