Kozuki Oden's Wife Being Alive

Based on the statement of kyoshiro "Oden's wife stood in front of castle" and cursed orochi, and the drawing as well looks as if oden's wife's face is towards the flames of burning castle, which possibly suggests that she herself was not inside castle and also as we can see it is shown many times that there are total of eleven graves of which three of them belongs to kozuki family which those graves includes the nine sheaths/swords of oden as well but what makes it more suspicious about oden's wife is that the third kozuki grave's name is hidden intentionally, which means if that third kozuki name was written a male or someone else other than oden's wife then we could instantly know that oden's wife is not dead.

Which if the time had came to introduce oden's wife then the introduction would lose all the shock factor since we had already known she was alive or possibly there might be another hidden intention of oda's.

And yes momonosuke did mention that even her mother suffered/killed by kaido's hands but it is possible that it is just that momonosuke thinks so but in reality she is still kept alive most likely because of the possible devil fruit powers that she had, which could be the cause of time travel, the curse that kyoshiro mentioned caused by devil fruit and judging kinemon's statement in the past samurais of wano didn't/don't know about devil fruit probably that is the reason kyoshiro and others thinks of it as a curse instead of devil fruit ability however kaido most likely knows what powers it is that's why she is being kept alive and probably wanted to capture momonosuke in order to blackmail her and also it is possible that this devil fruit and oden's wife could actually be the answer for all the crimes during the void century and it is her ability that might enable luffy and others to change the history of one piece world by traveling to past/joyboy's era.