I believe after a dog is dead and gone... it's considered finished.
There's really a lot of truth in that statement, Mike. I agree 100% with Monteria's take that to me a finished dog is one who has reached his maximum potential and likely won't ever be any better than he currently is (no matter if it's a strike, help, catch or whatever). Having said that, the majority of my dogs I wouldn't call finished. Do I have dogs that will flat out find a hog, won't trash (at least until I say they won't), have a pretty decent handle, don't fight, etc? Yes I do, but most of my pack are younger dogs that in my mind have not yet reached their full potential. Sure I like to catch hogs, but for me personally the best part of hunting is being able to watch my dogs mature and get better at what they do.
I also agree with Monteria, that people often will confuse a "finished" dog with one that matches a particular style of hunting. The oldest dog in my kennels is a 13 year old lacy/plott cross. I hunted him for years and to me there was no better. Over the past couple of years, my hunting style changed and I went to a deeper hunting dog. Now take the lacy and put him on the ground with my other dogs and someone watching would say he's absolutely sorry. Is he? Nope...he's just waiting for you to get a rifle and start walking with him through the woods. That doesn't make him any less of a dog, he just doesn't hunt the way I have come to enjoy.
A really good dog to someone might be a useless dog to someone else. It's all about matching the dog to the hunting style of the individual owner.