I think any realistic assessment would conclude that you run out of large game before you run out of cartridges. And that assumes some world-wide event that precludes anyone making cartridges, and/or the components used in reloading. Hard to imagine such an event. Local, mostly short term, shortages are not impossible but widespread and long term shortages seem unlikely.

If it comes down to it not much beats the brutal efficiency of gathering a community, tying crude nets, and using the majority of people as beaters to drive game into the nets where they are clubbed to death.

There are also snares, bows, spring and dead-fall traps, and endurance hunting where you run down and club the game to death. People have been killing game for a very long time and it is only the methods favored in the last few hundred years that would disappear, even in a worse-case scenario.

I realize debilitating shortages of ammunition and people living for years on large game hunting is a fixture in survivalist literature, and is often a working assumption, a 'given', in survivalist culture and boards, but I don't think that these assumptions are realistic.