In One Piece, does a Devil Fruit reappear after the user dies? In chapter 702, we see Ace's Devil Fruit 'Mera Mera no Mi' being showcased as the prize of the event held in the Colosseum. The announcer of the event mentions that the "fruit is reborn."

Does it mean every Devil Fruit has that ability to be reborn once the user dies, or is it an artificial Devil Fruit made by Doflamingo's factory?
Taken from the One Piece Wiki on Devil Fruits:


  When a Devil Fruit user dies, their ability is reborn into another fruit of the same kind. Instead of growing from a plant, the ability simply regenerates inside the closest appropriate fruit, as seen when Smiley "died" and the Sara Sara no Mi, Model: Axolotl transplanted itself into a nearby apple. Another characteristic of a Devil Fruit's growth is that the stem becomes noticably curlier than it was when the fruit was not endowed with the ability.


So, in other words, the Devil Fruit "respawns" when the user that had it dies.