I am researching UDID alternatives, and OpenUDID seems interesting.
I have done some testing and if I remove the app, and re-install again, the value of OpenUDID remain the same, I am just wondering how they do that and is the value always guaranteed to persist if I don't hard reset the phone.
Giving a quick glance at the naming conventions they use, I'd say they are almost certainly using the iOS keychain. This is the same as the OS X keychain, except it doesn't allow end users direct access the way Mac OS X does. Even if the app is uninstalled, this information will not be removed. It is stored in a controlled environment to prevent jailbreakers from getting it.