When we used to have chickens about 10 years ago, we caught 3 possums in the coop, which was on stilts in a 5 foot fence , they would climb it I guess (we had heavy logs around the bottom, and eat the chickens necks out. We finally got around to shooting them, had holes int he coop to prove it. We lived near "possum creek" if that tells you anything. They were road kill all over because there were no predators , too close to Atlanta.
That said , I had a horse get EPM, and possums are a carrier for the parasite that causes it ,and is shed in its feces and urine. I used to be a softie about killing--till I saw my beloved horse have neurological symptoms , he finally recovered, (only 30% do compleltely, 30% with neurological damgae and 30% get put down . )
So if you have horses, the last thing you want is possums around.
I now grit my teeth and aim for them with my truck......