Were all fairies exterminated?
According to the wikia page, some of them are still alive and living in the forest that Ban planted from the seed he was entrusted with by Elaine. There is a fairy realm and it is linked to the human world by the Fairy King's Forest.


  Several year later, fairies begin to inhabit the newly restored Fairy King's Forest after Ban planted the Almoca Seed entrusted by Elaine.