The Faithless are mortals who do not have a divine patron to speak for them. This is either because they never knew a god to worship, they chose to remain agnostic, their god had died (and didn't yet convert to a new patron), or simply that their god left them unclaimed(though this is very unlikely)
Unlike the False, the fate of the Faithless is unwavering: After being left unclaimed for ten days, they are doomed to be made part the Wall of the Faithless surrounding the City of Judgment on the Fugue Plane. Each soul is held together with a green mold from which souls cannot escape (but can be removed by an external force), and are slowly and painfully dissolved into the very substance of the Wall.
Notes:
In the games, you have a total of 5 faithless companions, and 6 if you count Okku (Though he IS a god himself, so that is debatible)