They grow wild in the woods around here. The plants sprout up early in spring and kinda look like groups of little umbrellas about a foot tall. Wikipedia has some photos. The flower (and fruit) is hidden under the leaves, so you have to turn over a leaf to see if the plant is blooming.
One thing I read online says that although they are edible, it's pretty tough to find ripe fruit, since squirrels or other critters are more likely to find them first. I've noticed the hard green fruits but never ones that seemed ripe.
I read about May Apples in a wild food book, but have never actually tried them. I got very excited when my son discovered a patch in our back woods this spring and I've been checking on it every month or so to keep up on its progress. Unfortunately they seem to have all wilted and died when it was like 100 bizillion degrees this summer. Sigh. Maybe next year.
You can eat these for sure, but I've read you need to be careful to let them fully ripen. The unripened fruit isn't so good for you and don't eat any other parts of the plant.
I've heard of May Apple jam, and I was told it was tangy. I don't think I've ever seen any ripe may apples. I suspect you are right about wild animals eating them. When I was a girl the hill behind our house was covered with them. We used to 'harvest' the unripe fruit just for fun. It never seemed to do any harm, they were back again just as strong the next year. Now I'd be more thoughtful about taking the fruit . . .