system
Given the following post, respond as if you're commenting on Reddit:
human
[ATLA] If the next Avatar is due to be a water bender, but every single water bender was dead, would a new water bender be born, would it skip to the next, or would there be no Avatar?
gpt
That was the logic behind the Fire Nation's genocidal assault on the Air Nomads, but as we now know, it didn't quite work out according to plan. There really is no way to know what would have happened if Avatar Aang had died with the rest of the air nomads, but there are a couple of potential theories as to what could have happened.

1) The Fire Nation was right, the avatar cycle ends, no more avatar.

2) Due to the linkage between the spirit world and the physical world, cosmic forces intervene to guarantee that at least one water bender survives to inherit the Avatar Cycle.

3) The Avatar Cycle moves on to the next element in the chain, Earth, giving time for the water benders to reemerge much as the air benders did a couple of generations later during Avatar Korra's time.

Thing is, genocide on the scale required to pull this off would me remarkably difficult, and it would absolutely HAVE to be Genocide. Unlike the air nomads, who had always had a very small population in relation to the other nations, the Water Bending tribes were not isolated to small, localized regions. Due to their lack of numbers and tendency to remain in the vicinity of their temples, the Air Nomads were remarkably easy to kill off. The Water Tribes, however, were far more prone to sea travel, spreading to islands all over the world and also intermingling with communities in the Earth Kingdom. There were also the swamp dwelling benders Avatar Aang encountered during his travels, who were almost entirely isolated from other nations by their environment and virtually unknown to the wider world, so really it's just impossible to conceive of a situation where every single Water Bender on the planet would be dead.

TL;DR your question is impossible to answer in any satisfying manner.