What happens if units from both sides in combat survive, either because of Kayn or a stun?

In this case, both sides will still assign damage to the other side as normal (stunned units will not deal damage). Units will still die if they are assigned damage equal to or greater than their Might (unless they donʼt die, for example because of Kaynʼs ability). Then if units from both sides remain alive at the battlefield, any remaining attacking units will be recalled to base and the defending player will maintain control (no score, though).