My pigs don't go out unless we're here, we have a fox family at the end of the garden.
I bought a rabbit hutch to go inside the run but it took up too much room and was a nightmare to get in to catch them (DD has to go into the run)
We have 2 run&house set ups (we have a 3+2 pig families) .
DH fastened some of those ring hooks to the hutches and attatched to the bars with kabinas (sp) those lockable twist-fasten climbing hooks .
The hutch has extra layers of wire and the doors are fixed, we open from the roof which is lockable.
Little house has a lift up roof (locked) no windows.
For the doors I use cable ties (have to cut them so they are single use but secure)
For fox safety, what about a mesh /wire skirt round the run. You could wire it onto the run (out of reach of piggy eyes) and extend it all round about 12" wide , pegged into the grass (we use hard ground pegs, hammered into the soil)
A few weeks ago, our boar just sat there 
while a fox sat beside the run (I thought it was a cat, did a double take and ran yelling down the garden)
At school, he'd have had people round all the time to protect him. Foxes can cause huge damage (utter vermin IMO) one of my guinea pigs was dug up twice . Luckily his body was in a sealed bag so they didn't shred him. But he was buried in a deep hole with things on top. They dug under from the side , the shrubs didn't even stop them.
At the moment, my pigs like being out in the evening and are more active at dusk.
DD puts them out after school if I'm at work, they are still troughing grass at 10pm if we let them 