From the rule book:
"If all of a player’s participating ready units are exhausted, but his opponent’s are not, the opponent continues to focus and strike with his ready participating units, resolving one strike at a time, until all participating units are exhausted."
Essentially all of the participating units in a conflict must be exhausted before it ends. If the unit has no icons, it still strikes but nothing happens.
Also from the rule book:
"Any participating unit (attacking or defending) that has not been destroyed by the end of the resolve strikes step is considered to have survived the engagement.
If at least one attacking unit has survived, and there are no surviving defenders, this is an unopposed engagement and the attacking player deals one bonus damage to the engaged objective card. This is known as an unopposed bonus.
if the engaged objective was destroyed before the reward unopposed step, there is no unopposed bonus."
Any unit can grant an unopposed bonus, as long as there are no defenders. Icons do not matter in this regard.
BTW, Divinity how are you liking the game?