As previously stated, totally free ranged chickens are never safe. BUT having them in a coop or run doesn't mean they'll be 100% safe, either. If the run is not enclosed on top, birds of prey, coons, fox and other various critters can come in over the top. If it is enclosed, there is still a chance of a weasel or other small predator coming in through that one small gap that you missed. Everyone loves chicken!
Someone stated above that "if they're totally free range there won't be a run". Not necessarily. You can still have a run and let them out of it. That's what I do. I have two coops (an 8x2' shed and 8x16' shed, actually) with attached 12x16' runs. The runs are there for the occasion that my son & daughter-in-law come to visit with their golden retriever who is not trained to be around chickens. Or for the occasional time that we're gone for a few days and don't have someone to let the chickens out and shut them in for the night. My chickens free range whether we're home or not, and until this summer, we have not had a problem. We live in a rural area and have coyotes, mink, weasels, hawks, eagles, skunks and possums around (and probably a few other things I have forgotten about). We have had a dog until June of this year when we had to put our 10-year old lab down because he had cancer. In July we were gone for a full 2 weeks (my mom was coming over and letting them out to free range in the mornings and locking them up at night) before the local coyotes figured out that there was no one around and took out 4 or 5 of them. They were kept in the run until we got home the next day, as Mom felt terrible. To answer your question, we keep the coop's pop door open 24/7 in the summer. I have closed it this past week with our cold temps, but you will most likely not see that kind of cold where you are ever, so you wouldn't need to worry about it. The pop door opens into the run, and we just open the run gate to let them out. Another nice thing about having a run is they can go out in the morning and not have to be...er, cooped up until we get out there in the morning.
Edited to add - we do have a cat that gets into the coop through the pop door and steals eggs when she gets a chance. She helps keep the rodents down, though, so I don't mind sharing with her now and then. If I don't want her getting any eggs, I keep the run gate shut until they're done laying for the morning.