You will receive Trade Quests to 'Fix Broken [...] stone statue'. When you turn it in you will receive the sculpture.
Hime Stone Statues (a.k.a. Buff statues) can be created via a quest which requires 1 broken statue This item is only dropped if you encounter and defeat a Hime as the last enemy before the boss fight. You must then carry on to defeat the boss to claim your prize.
For those that drop at Sculptor Mountain see:
For all others: