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.
If I were to use Your Clan Needs You! to bring in a Crab Samurai, and then delay his destruction with Razor of the Dawn Castle, after the battle he would return to the Province.
What happens to him at the end of the turn if I then buy him in that Dynasty Phase, and what happens to him at the end of the turn if I instead leave him face up in the Province?
If I were to use Your Clan Needs You! to bring in a Crab Samurai, and then delay his destruction with Razor of the Dawn Castle, after the battle he would return to the Province.
I'm not quite sure if you are describing a scenario in which you are using Razor of the Dawn Castle in response to:
A) Your Clan Needs You! In that case, using Razor of the Dawn Castle would be illegal, because Your Clan Needs You! does not destroy anything: it discards.
B) Some other destruction effect occurring in the meantime. If that's the case...
What happens to him at the end of the turn if I then buy him in that Dynasty Phase(?)
It would be destroyed. All of the effects that were activated on the card are still activated (http://rules.l5r.com/CE_Physically_marked_card_states, http://rules.l5r.com/CE_Effects#Effects ... ut_of_play). Just being out of play does not cause loss of card memory (http://rules.l5r.com/CE_Effects#Tracking_rule).
(W)hat happens to him at the end of the turn if I instead leave him face up in the Province?
This one I'm kicking to the Rules Junta.
On the last question, current thinking from the Rules Junta is that an out of play card can still be destroyed. This is unusual, because out-of-play cards are not usually eligible for targeting.
Thus, a Personality whose destruction was delayed by Razor of the Dawn Castle who ends up out of play (but not face down) when destruction is scheduled to occur will still be destroyed and go to the discard pile.
There may be an update to wiki to reflect this in the near future.