These avatars become strongly associated with a specific member - almost as if it is that person's trademark. In some cases the avatar may be highly unusual or creative. Sometimes it is quite simple. Yet its association to the particular user is so strong that others experience it uniquely as that person. While trading props is a common practice, the owner of an idiosyncratic av rarely gives it away. It would be like giving one's identity to someone else to use. Other conscientious members also don't "steal" (i.e., screen capture) an idiosyncratic av and use it as their own. They respect its integrity. If someone does steal and attempts to wear an idio av, they must be willing to put up with criticism by the friends of the owner.
http://www.rider.edu/users/suler/psycyber/psycyber.html