I went out early this morning to check things out, and I think I know how that possum got in. Just like how burglars get into your house - through the front door.
The run is chainlink, as is the gate. The gate doesn't go all the way up to the top, so the opening had hardware cloth over it. It used to be tight. I have now realized that over time, with constantly opening and closing the gate, it isn't as tight as it used to be. And I never noticed. It would be tricky but not at all impossible for even a large possum to find his way in there, with determination. You know, for two people who are fairly good at improvising, why didn't we find another way to make that gate safer? It took me two seconds to realize that I should have just extended that gate - both in and out - with something stiff (like a wire cookie drying rack, I have plenty of those). And I should have noticed that the gate wasn't as hard to close as it was previously.
The top of the run is covered with hardware cloth and chicken wire and it's all criss-crossed in layers and zip-tied. We used to joke that it was like Alcatraz. It looks like a prison. So I don't think the top was the problem.
