Non-Unicorn characters with a positive number of Courtship Points who are left unmatched will be engaged to members of the Unicorn Clan who are not present at the festival, while those who have a negative number of points will be sent home with an apologetic letter from the Unicorn, unengaged and quite shamed. These characters will lose Honor as if they had committed a major breach of etiquette and will gain 1 rank of Infamy.
Sounds like Unicorn characters with negative points are still available just fine, which makes sense being their house.