For myself, I live in a rural part of Texas, in the hill country, but this county alone has 30K people, and the ones bordering it do too. We're about 1.5 hr west of San Antonio - a few day's walk down I-10 or about the place a half tank of gas will run out. There are MILLIONS of people who will be leaving the cities. what I see is after the food stored and scavenging run out, people will turn to hunting, but with no food storage, each deer(and there are a ton) is going to go bad in a day. how many deer each day would you need to kill to feed 30K people? even if it were just the locals. Not to mention scenarios where there's disease or radiation or some other chemical affecting the animals.
I'm partly basing this off what I was told by an older East Texas man, that during the great depression deer were virtually wiped out in the forests due to sustenance hunting. And there's a lot more people now.
Those 30k people will be much less within only a few weeks. Most people dont have enough food, or water to sustain more than a week. They also dont get the concept of rationing.
Add in that the population number includes alot of people who require medical treatments, and medications to keep themselves healthy. Some conditions will quickly decline without medication and/or a very specific diet that cant be maintained when you dont have options like a grocery store and pharmacy.
The knowledge and experience of hunting and foraging is lost on aloy of society today. People have gone soft here with the availability of packaged food and meat they never had to kill and process.
Average people wouldnt even know how to create a fire without a Bic or a box of matches.
The elements will eliminate a good portion of people
Common illnesses that would normally be treated quickly and easily are now deadly or incapacitating. They will also spread quickly.
All of this plus the violence of desperate people will decrease the population so much that i really doubt the wild game population would take a huge hit.