In OK deer are considered property of the land owner. If you shoot a deer on your property and he makes it to your neighbors property, you have to have permission from the landowner to retrieve the animal. If the landowner refuses you have to let it go. If you go get the animal you can be charged with trespassing, and hunting without permission. If the GW is notified that an animal is being left to rot I am not sure what they would do. Depends on GW.

I have hunted in SD and it is a law that the sportsman retrieve his game no matter where it goes. You can't take a weapon on the property but you must attempt to recover the game.