Yikes! I would never touch a ground squirrel and I certainly wouldn't eat one. I have absolutely no issue eating tree squirrels and they taste just like,,,,tree squirrels (humor). As far as what happens to them after they are shot; coyotes and other squirrels will take them away and eat them from my experience. And no, I am not really concerned with the Plague. Haven't heard much about that for some time, but rabies are possible and fleas are a certainty. I just joined this forum and I wanted to share a recent experience that maybe you hadn't experienced.
So I live in far-northern Kali and yes, I have hunted the vaunted McDole squirrel fields and they are real. Benched on a table or sticks, I started with an open site 1936 Remington model 341 rifle, then moved to a .22 magnum Marlin for 125 yd shots and then to the 22-250 for beyond. It's all good, but with time, cataracts slowed me down. Today, I do my bidding with a .22 pellet rifle out my shop building to the wood pile that is maybe 35' away.
Yesterday I was doing a dance with a brown and it knew the score so it wouldn't show after I opened the door. The Gamo was rested and the lites off, but it knew better. I have internet in my shop next to the woodpile and I had a thought; what if I Google squirrel calls and turn the speakers up? Well I did and sure enough, he rose up and stayed up. Lots of ways to skin a cat. I will add a cam to my CCTV system that will point where they show. It doesn't always have to be the quantity of kills to make my day.