@theoldchick is correct, it doesn't take much for them to switch to chicken dinners.
They're very much opportunists, and will gladly take the easiest meal. As long as that isn't a sleeping chicken, eggs, or a couple chicks, you're fine.
Be aware that just like feeding stray cats, feeding possums can be an increasingly large past time. The females have frequent, large litters.
Everything that follows is NOT something that I recommend, happened a long time ago, and may violate your state laws, so please do not take this as a recommendation. Just humorous anecdotes from my youth.
My grandfather farmed a few hundred acres at one time, and in my later teen years he'd stopped farming, but still had the habit of maintaining an army of barn cats. He fed these on his porch, and also had a collie nearby. The collie would fend off most of what might bother a cat, but the possums were perfectly happy to thread the needle between the dog and the porch, and take possession of the cat food.
I had an affinity for most living critters, and my grandfather would call me to collect possums from his porch when they got excessively prolific.
At first when he taught me to capture them, I'd wear a welding glove. Later I'd catch them as he did, bare handed. Again, I'm not recommending this. They've got a face full of teeth and while they rarely carry rabies, they frequently eat well rotted road kill.
Snatching them by their tails and lifting them into the air requires surprisingly little effort. A small "bounce" if they try to curl up and bite returns them to a downward hanging position.
Now a family of possums hanging by their tails while they sleep is a very Disney image, but looking back, I don't know that I've ever seen a possum assume this position willingly. It didn't seem to cause then distress, but I don't know that I would still consider this to be a safe and comfortable way to handle them today. And possums may legally be a fur bearer in your state. Check your laws before you decide to interact in any way.
At the time I would drive them off a mile or two and release them. Possums don't have a wide travel range, and it doesn't take much for them to not come back. Again, this isn't something I would recommend today. Wherever you drop them off, there's already going to be something living, and now you're introducing a new mouth to feed, and possibly diseases.
As a teen with an interest in animals, and a grandfather with a similar mind set, some of those possums were held for a bit rather than immediately transporting them. About 10 minutes of handling is generally enough for the possum to switch from "help! I'm being attacked by a predator! " to "humans are good for scratching ears".
Now I don't think the possums really sought out human affection, no matter how socialized they became. However it is easy to convince oneself that your holding something closer to a very calm cat than to a wild animal.
A few years later several of them ended up riding around in my car as I went to college. And then riding around campus sitting on my shoulder. One at a time. Not several all at once. That would be ridiculous!
Again, I really do not endorse placing an animal on your shoulder, particularly where that animal was 48 hours earlier roaming the woods and scavenging your grandfather's cat food.
So possums are surprisingly malleable behavior wise. They're surprisingly easy to tame. Harding Magazine (publishes Fur-Fish-Game) at one point, and maybe still, has a fur raising book that describes propagating them as a fur bearer. There's a history of cultivating them in captivity, at least for a very niche market.
And also if they get hungry they'll drive your cats off their feed and eat your chickens.