As has been mentioned but never explicitly stated, trapping will fill a pot much quicker than hunting. Using rat traps for birds and even squirrels is possible, but nothing beats a dozen conibears in various sizes. There is even a way to use a larger model of conibear (330) to get deer. Definitely NOT something to practice until absolutely needed as this would violate almost all state hunting/trapping regs but in a life-or-death situation, the rules go out the window.
This thread reminded me of an episode of "Jerico" where one of the lead town folk stayed in the woods for several days trying to hunt for deer but after a few days his wife brought him some food and said " I thought all the deer were gone?" He replied, "they are, but I was just hoping".
After some time into a true wrol / shtf situation (maybe a few months to a year) most if not all wild life will be hunted to the point of extinction.
If you have room, raise some chickens and rabbits for meat.
Don't forget about fish! Convert an old swimming pool into your new fish pond.
In my humble opinion I believe that wildlife will not be decimated because many do not hunt or get outdoors like that should and learning in a worl/shtf scenario may not cut it for that sort of thing. Who knows though.
accidents? Ha, people will shoot you on sight, quite deliberately, pard! They will want to remove you as a threat, and to not have you competing for resources, or just for the hell of it. Only about half of an animal's live weight is edible meat, and under stress, each adult needs 4 lbs of food per day. So you'd have to catch 8 squirrels per day, or 4 big rabbits, every day, or kill a typical (100 lb) deer every 2 weeks, for every adult in your group. Far, far better, is just to keep your eye peeled for game, your silenced rifle ready for a shot, but have 40+ traps, snares, nets, trotlines, etc ready. Better yet, have night vision capability and "tend" your traps and nets at night. Set them up in loops, like a 4 leafed clover, so that you end up near your "base camp" 4x per day. Use poison to kill off the predators that are eating your game. Use jacklighting and bird "lime" to trap roosting birds. Look for nests and eat the eggs, in the spring. Realize that you'll have to eat insects, reptiles, amphibians, all sorts of goop. Have at least a 6 month supply of buried food. Know your wild, edible plants, be set up to grow and use sprouts.