Simple, Can you seiden sanzo one of the created personalities. As the cost to destroy will never occur
Earthen guardians
A topic from AEG's L5R CCG Rules forum, copied for Oracle of the Void from a copy of the forum saved in October 2015, so pages it didn't save are missing. Players' names are left out; the rules officials are named. Rulings are as they stood on these dates; later rulings, the rulebooks and the Rules Archive may differ.
Simple, Can you seiden sanzo one of the created personalities. As the cost to destroy will never occur
Not so simple, I'm sorry. You seem to be operating under a pair of misconceptions:
First off, Earthen Guardians creates a Personality as a Battle action, then removes it from the game at the end of that same turn. Unless you fight a battle during the Action Phase with Ambush or a similar card, there's no easy way to take the Limited action on Seiden Sanzo between the Guardian's creation and removal. Perhaps you took that as a given, so let's move on...
The bigger issue is that the destruction from Seiden Sanzo is a delayed effect of its action, not a cost. If it were a cost, it would come after the first colon ("Limited:") and before a second colon, in the constraints block (Citation). However, there is no second colon; Seiden Sanzo's action has no constraints block, only the required target of a Personality you own and control in its effects (Citation).
Edit: Changed slightly, because my first draft disregarded the existence of Ambush and the like. Silly me.