What happenes to honour structures once durability is 0%?

When honor structures are attacked and destroyed they will disappear and be 'recalled'. Any benefits of them will stop. The owner can then replace them on the map in an available place (the area may need to be cleared of enemy plots first). The replaced building will work again but will need to be repaired to bring it back to the full durability. This costs stone. If you don't repair it then it can be destroyed again in 1 hit.