After finding all the runes, fairy chests instead give stat boosts. Are these boosts applied to only that character, or are they a permanent boost to the whole bloodline?
I have tested this with a Hokage. Prior to the Fairy Chest, he had 171 Strength. With the permanent stat bonus of +1 Strength, that got bumped to 173 Strength.
I then fed successive generations to the castle until I could get another Hokage. I checked their strength stat, and it was at 173. So, yes, fairy chest stat boosts apply to all characters going forward.