Antelope sheaths are made up of keratin, the same stuff as your hair and fingernails are made of.
Antelope bucks drop these sheaths usually at the end of the rut, and they start growing them back immediately.
As stated mice and small rodents love to eat them, full of chemicals, i.e. protein, so they don;t stay around long.
I've been lucky to find a couple out on hunts, and I use them in our Hunter Education classes to show kids what they are and how they differ from horns and antlers.
Here is a question to ponder. What do you think the legality is of shooting a buck in Arizona that has just dropped his sheaths?
It happened here in Kingman, many years ago when a lady hunter had been watching this buck all summer, then on her hunt, she saw the same buck buck, but he had recently dropped both of his sheaths... She shot him anyway (I know, what the heck was she thinking?) I did a story on her in our local newspaper, what do you think G&F reaction was?
Don Martin