I guess let me rephrase the question. Does there exist system that is inconsistent but the inconsistency is localized and therefore we can actually miss the inconsistency by not knowing or noticing the localized inconsistency? Is there a proof of what you said as well? An inconsistent system with the inconsistency in one spot can have any statement made about the system be both true and false? I’m adjusting the parameters here so we can ask the deeper question of whether one exists in the real world.