In the beginning, Hylia & her husband bestowed upon the Hylians & Sheikah a blessing. If ever one went extinct, then the other would bring about their revival. For they were sister peoples in all things.
So, the only way to truly end one of the 2 peoples was to also end the other as well.
For they were 2 sides of the same whole & one could not be without the other. Much like Yin & Yang.
Therefore, if Sheikah were to thin out or even die off completely, then Hylian women would begin to give birth to new ones. Not in an asexual reproduction way, the new Sheikah would still have fathers.
The same is true vice versa.
Though, this doesn't occur normally & is really more of a self-preservation mechanism.
The reason that they can even do this is because the 2 peoples were originally created in conjunction by Hylia & her husband mixing their life energies together (not sexually, more so in a spiritual or magical sense). Thereby making them literal sister people.
Of course, the Hylians' primary creator is still Hylia & in this way, they took more after her. However, the same can be said of the Sheikah & Hylia's husband, Sheikishin, a.k.a. the Fierce Deity.
LoZ Cultural Masterlist 2