This is a question that no one can answer for sure for you. Many predators, bobcat, coyote, fox, mink, dogs, raccoons, skunks, and many other are often out hunting during the day. I’ve seen all these during the day. I even saw a possum once feeding form my compose pile at 1:00 pm on a bright sunny day. That one surprised me. There is more danger at night for various reasons, mainly there is less human activity so they are bolder. But there are posts on this forum where a fox, coyote, or something else snatched a chicken just a few feet away from where a human was standing. That kind of thing can happen, but does it happen that often, not really.
Larger predators like coyotes, raccoons, dogs, bobcats, maybe fox or mink, can tear chicken wire. The heavier the gauge of the chicken wire and how well it is attached are quite important in this. Chicken wire will provide a lot of protection against many predators, so it is beneficial. Which predators will show up for lunch, I don’t know.
Many of us use a philosophy of a predator resistant run during the day and a predator proof coop at night. It works pretty well for most of us but it is not totally fool-proof. The more predator resistant you make your run the safer it is. How precious are your chickens, would you or yours be totally devastated if one were take or are they more livestock than pets? The more predator resistant or proof you make it, the more it generally costs. What is your risk tolerance? There is no definitive answer to your question. It’s a decision you have to make.