What I would like to see happen...

I'd love it if he went after Rand, but due to the wound Fain gave him he finds it impossible to fight. The wound bursts open and is starting to kill him when Moridin appears from nowhere and kicks Fain's butt. Moridin is also wounded in the fight...both he and Rand are too weak and close to death to move. Nyn shows up, Heals both of them (not knowing that Moridin is a big bad), but instead of being concerned about each other, they look around for Fain, of which there is no sign. I'm a bit partial toward what comes next because I ran an RPG based on the idea of Fain being the big bad in the Fourth Age, but...

Cut scene to Fain with black mist fading from him. He's weakened and realizes the fight is over for now. He starts heading toward Shara with a sly smile, thinking about the destruction he will cause with thousands of channelers.

What I think will actually happen is that he'll either be killed at Shayol Ghul (probably by tripping over his own feet or something equally as stupid) or he'll end up being offed by someone who isn't really worthy of taking him out (Moiraine, Egwene, Cadsuane, Min, etc.).