You're right about the leftover tags. I was down in 34B a few years ago (3 years I think). We didn't see any illegals. We saw lots of Border Patrol agents, quite a few hunters, and absolutely NO deer, rabbits, quail, birds of any kind, or any game at all. Not even a stringy old jackrabbit. Only talked to one hunter while gassing up in Sonoita on our way out, that even saw a doe. And he said he saw her standing next to the highway when they drove in on Thursday morning.
We only heard one shot all weekend, and we found out (from talking to the guy that fired the shot) that was from a guy that saw a coyote (4-legged one) from far off and took a shot at it.
There was no grass, and no deer sign or tracks anywhere. There was a TON of cows, cow tracks and cow patties everywhere however.
I'm not really in a hurry to go back to that area again.