I have eaten possum, but not since I was a kid. I trapped and kept alive any large possums I caught. I placed them either in a coup or in a trash barrel with leaves on the bottom for them to say on and "purged" them by feeding table scraps for several days similar to what Dave Scott posted about. My grandfather would make the phone calls for me and one of several gentlemen would come by the house to buy them for food. I don't know how many I trapped in my youth, but had to be at least 2 or 3 hundred of them. I think I got as much as $3 for the bigger ones, which was a lot of money to a little kid in the late 60s, early 70s. I did have someone bring me some "possum stew" once and though I don't remember what it tasted like, I don't remember it being bad. I do remember them saying the meat has to be boiled and the fat poured off before cooking.
To this day, it is not unusual for me to see a possum, run it down, grab it, run back to the truck, tent, camper, whatever, throw it in the door, slam the door shut, and stand back just to see what the people inside will do.