Well, as the deer die off there are more resources left for the remaining deer, and so it is easier for them to have kids and the birth rates might increase. So it could potentially converge to a predator-prey equilibrium
Which were intentionally hunted to near-extinction and the carcasses wasted as a method of suppressing Native Americans.
Compare to whitetail deer: most hunters are interested in big trophy bucks and only bother to shoot does because they're part of a game management system. Killing does is for population management, and a lot of hunters aren't doing it just for food, though the does have milder flavored meat. They don't want to kill one, drag it out of the woods, take it to a processor, pay for processing, and then go back and pick it up a few days later just for the meat. Hungry people, OTOH, might not care so much where they get meat if it's free or very low cost to them.
One problem that can occur - and why these programs can be challenging to run - is that there is no control over the time between killing the animal and having it given to the processor. In colder climates, this is not a big issue as many will field-dress the animal to reduce weight and allow it to cool naturally. In warmer climates, it might be well above freezing even during winter hunting seasons. Killing the animal, dragging the carcass to a point where it can be field-dressed, and transporting it to the processor could take hours, increasing the risk of contamination.
> a lot of hunters aren't doing it just for food, though the does have milder flavored meat.
I know both hunters. Some want the trophy, some want the meat. Those who want the meat prefer does if they can get them for the milder meat.
This is somewhat cultural though. I grew up in MN where limited amounts of doe permits were always given up - thus every hunter made sure they applied for the yearly lottery for doe permits and so a culture of hunters preferring doe meat when they could get it developed. Next door in Wisconsin they never gave doe permits and so hunters learned "don't shoot the doe, one buck surviving can breed it thus resulting in deer for next year's hunt". Now that population control is important MN had no problem giving out more doe permits, Wisconsin had to force the issue (no shooting bucks until you shoot a doe) as even when hunters were told they could shoot does they didn't.
