Avatar: The Last Aibender‘s main magic system rests on the four classical elements and their manipulation. However, as the show progressed, the bending arts revealed a slew of sub-bending abilities that created a more complex magic system than what the story initially let on.
At the beginning of the series, we learn that Ozai took it upon himself to wipe out the Air Nomads, who were rendered extinct in their entirety, save Aang. However, a new theory suggests that a slew of Airbenders could have picked up a more settled lifestyle in the Earth Kingdom, and could have become the sandbenders that we see in the show.
The sandbenders in Avatar: The Last Airbender have a similar bending style to airbenders
Sandbenders have a lot of similarities to airbending when it comes to the bending arts. Air and Earth find themselves on opposite ends of the element spectrum, being as opposed to each other as fire is to water. While airbending requires the user to be free-flowing, embracing concepts of freedom, earthbending is easier for those who are of a more stubborn outlook. Earth is the element Avatar Aang has the most trouble learning, given how against the grain it was for him when compared to his Air Nation philosophy.
Sandbending seems to take a lot of its cues from Airbending, being a subbending that is difficult to master even for prodigies like Toph. However, the abilities could have developed when Air Nomads, following the migration cycles of SKy-Bisons, settled in the desert and picked up a unique type of bending while staying with Earth Kingdom citizens. This allowed this niche fact to develop sandbending.
It is possible that air nomads hid among sandbenders during their persecution by the Fire Nation
Air Nomads definitely fought with the Fire Nation when they invaded the Air Temples. However, it is difficult to believe why certain members of the temples did not simply escape. It is possible that a lot of them could have fled and hidden with other nations, especially with the sand benders, as it would have been easy for them to mask their bending. There was also the matter that the desert was not somewhere the Fire Nation would expect to go looking for Airbenders.
In the hundred years that Aang was missing, the air nomads that fled could have assimilated completely with the sandbenders, which would have allowed them to stay hidden from the fire nation. Aang’s return would have been inconsequential to them, as more than a few generations would have passed, causing them to dissolve their identity as Airbenders completely.