IMO, after the Bore is sealed, and the Light side returning south to recover their depleted army, Demandred will invade with the Sharans (yes, waiting until after TG is done). This will create a "Scouring of the Shire" sort of ending, a tribute to what was possibly the best part of LotR.

Alternatively, Moridin might survive. It has been more than hinted that he is the yin to the Dragon's yang - they will meet in many turnings of the wheel. So I expect he could survive.

The other possibility is that he lives on because of the link he has forged with Rand - perhaps if my previous theory about rebirth is wrong, then he is trying to enter the rebirth cycle by linking himself to Rand. This doesn't make much sense given his conversations in tGS however, although the meeting with Rand reeked of a ruse used to get Rand to start using Balefire. I think that the DO actually wants Rand to balefire himself (the DO) - this would kill the DO forever, effectively halting the wheel and destroying the pattern. The moral being that a perfect life is no life; we need to have challenges and conflict to keep life going.