I notice this was posted on the KY/TN board, so there are regional "specialties" in that area. Another poster cited ramps, which are a kind of wild onion. Most often chopped and added to scrambled eggs. Offal is used extensively in rural communities. Fried young squirrel is common; beat the squirrel with a frying pan to smash the small bones before frying.
In my part of the country, you won't get the unusual foods in restaurants because the health departments don't approve the potential sources for the meats or some of the vegetables that other folks would call weeds.
The regional Ramp festivals are one of the few places where ramps are readily available; for meats, you need to be in a place long enough to make friends and get invited to eat smoked groundhogs (also called whistle pigs) among the many wild critters that are locally edible.
Were you to buy land and allow your neighbors to hunt, you'd learn such minutae, but it takes time and patience.