I would think one would have to do this on a case by case basis and look at the overall condition of the animal.
While many people claim predators eat the sick and lame, I've generally found this NOT to be the case with animals that were very sick and feverish. We had many, many deer die here of EHD in the past two years, and very few of them were touched by the resident coyotes, racoons, possum, skunks, etc. The only ones I saw that were chewed on were the ones in the creek, and I believe that was by turtles and crayfish. Once the deer were pretty much decomposed and nothing more than dry hide and bones, the scavengers would scatter them around. But, shoot a deer and leave it overnight and you may get a head and spine for your efforts. We also had a small buck that was injured, I believe it was hit by a car, and very lame and feverish acting when I saw it. I found it two days later laying in the edge of the creek and nothing touched it above the waterline.
I think most animals avoid eating feverish animals to prevent spread of disease - of course if the scavenger is starving, anything's fair game. I think predators are like us and prefer fresh, healthy animals.