system
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human
[ATLA] Did each of the four nations only have benders of their respective element? Ex: Were there any earth or water benders living in the Fire Nation legally?

If so, why didn't they aid in the war? Earth benders with allegiance to the Fire Nation would have been very useful in breaching the wall around Ba Sing Se.
gpt
Bending is as much genetic as it is spiritual, so some of the nature of bending passing between generations is up for debate. But yes, it seems like benders of one specific type congregate and have bender children of that type within the confines of their nations. 

Cross-bender migrations and contact happened before the war, as evidenced by the swamp benders being a long-lost group of waterbenders far from the poles. (and perhaps sandbenders learning airbender techniques to augment their natural earthbending) But it's very probable that 100 years of constant fighting with the fire nation consolidated and segregated the remaining bender population. Especially since the firebenders held themselves to such a supremacist regard, and seemed unwilling to use other benders as allies except in very specific scenarios, often ones where the firebenders are clearly in a superior position. (referencing the way Azula used the Dai Li)

Waterbenders would not have been able to live in the fire nation, since it was accepted knowledge for many decades that the previous airbender avatar was dead, and the next would be born a waterbender. That's why the southern tribe was so brutally attacked and stripped of its benders. And the north was barely strong enough to resist, but it would have come under heavy assault even without Aang's reappearance.