and a game continues to be fun when there is no way to fully win.
No. That's when it starts getting pointless. It would be like a second life, which would suck you in for eternity.
Play it a while. I'll bet you'll get bored of it pretty soon. But that's just dreaming, and probably won't happen for another hundred years.
Really? What would be the point in play a game that is in effect unbeatable, and offers no new experiences? Wouldn't it be just like IRC, but in 3D? Wouldn't it then be better to meet people in real life? Maybe play a round or two of Super Smash Brothers Melee or something?