N-US056, when sent out to Attack as the Head Ninja, sets a condition that is applied after the Showdown, before the Return, after Battling ends. The effect, when activated by being sent out to Attack, does go on the new Chain and can be Chained to by effects with the correct Timing. if injured before its effect resolves off the Chain, will not be applied. after the effect resolves off the Chain, the condition will be applied no matter if N-US056 remains in play.
N-055, when opposed by a Head Ninja will also activate and go on the Chain. If the effect resolves off the Chain, the effect sets a condition that will be applied later in the turn no matter if the Ninja is still in play or not.