A sad update...
Well, I did catch that raccoon the same night as I was typing up my first post. Found it curled up and seemingly asleep again in the older of my two live traps when I got home and I went in the house and got myself settled and changed clothes, then came out again to go deal with it. I was actually in a good mood. I'd caught the raccoon (yay!) and was starting my four-day string of days off and would now feel safe letting the chickens out and spending a gardening day out with them.
When I initially lifted the trap with the raccoon in it, it sluggishly came awake and moved to sit in the trap end furthest away from me. It also turned out to be bigger than I initially thought--a yearling female. It was just that it was so thin and narrow that it seemed a good deal smaller when all curled up and all you saw was a ball of fur. It did seem sick, pinched about the face and its ears seemed droopy, and had very bad fur even for an animal that had recently come out of hibernation...thin, standing-on-end, 'dead' fur. I could see something red in its belly area--it was sitting on its haunches, back feet out--and it took me a minute to really figure out what I was looking at.
The red thing was all that remained of its right foreleg, the part analogous to our forearms. No paw or wrist left, just a horribly swollen mass with its uppermost part ground halfway down into the muscle and with a couple of inches of the thinner forearm bone sticking out. Its right hind foot had also been badly injured with a terrible wound on its top and was likewise very swollen. To top it off, the poor animal had a bald divot gouged into it's head between its ears.
The only way I can think of for it to incur such wounds is that a large truck ALMOST ran it over and that one or both tires on one side caught its right foreleg and right hind foot as it either froze in place or maybe even dodged as the vehicle passed over. The undercarriage could have cracked it one across the head too.
The hell of it was that the wounds were very clean and free of localized infection and shreds of dead meat...even the bone sticking out of its forearm was sparking white. The raccoon had clearly been doing her very best and licking her injuries diligently and the flesh wounds were actually healing...they looked about two weeks along. An amazing example of an animal's trying to survive and by far the worst injuries I've ever personally seen any wild animal trying to cope with. But also hopeless. A partially amputated foreleg and a badly injured hindleg, both on the same side... I can't imagine the suffering that raccoon was going through just trying to walk and I'm glad I didn't see her try to do so. I also think she was starting to fight a more generalized, 'blood' infection, hence the sluggishness, rail-thinness, and 'dead' hair. I put her down as quickly as I could after seeing all that and consider that it was a mercy killing on top of just putting a potentially dangerous chicken predator down.
So, as it turned out, that raccoon did indeed have a very good reason for behaving in a manner which I considered suspiciously abnormal. I just wish it wasn't such a darn sad reason...sigh...

She reminded me of those pitiful animals you see in Africa sometimes, the ones that get caught in poachers' snares and who only manage to escape at the cost of one of their limbs. They never last long either, normally, unless they have human help.