Unfortunately, animals that you've never seen before will eventually discover the tasty chickens out there and will try to get in the run (The problem with chickens is that literally everyone thinks they taste delicious!). Most people in predator-heavy areas use hardware cloth on their run, as it has small enough holes that predators can't reach their paws through, and is a heavy-enough gauge that determined predators can't tear through. (Something like this:
https://www.amazon.com/dp/B015PD9JX0/?tag=backy-20 )
You can use electric (live) wire around the run that may deter some predators (search online for "electric fencing" or go to your hardware/animal feed store and ask about it).
Some people have a guard dog for their chickens who will watch the chicken area at night and run off any predators.
If you put them in the coop each night and keep the cooped predator-proof, that would help, but some predators get bold, and attack in the early morning or evening before the chickens are in the coop.
I just don't want you to wake up one day to a nasty surprise!