I'm not sure if it's ever been printed but I've heard it said by many JWs that when the UN turns on religion everyone 'claiming to be a Christian' (not a jw) will immediately give up their religion. The think that they are the only ones who will refuse to compromise, that they alone are loyal to God. Everyone else only practices their religion for show or personal gain, once persecution starts they will abandon their beliefs in a heartbeat.
Apparently Satan (or the UN?) will see that JWs are the only ones still practicing their religion after the UN ban and, just as they are about to turn on them, they are destroyed by Armageddon.
I'd really like to know if it's an official teaching. If it is, it's probably one of the most ridiculous, deluded, insulting ones yet.