The Sheikah are an enigmatic tribe, with very little about their history being known. However, ALBW offers a possible clue. Hilda, the princess of Lorule, has red eyes (a racial characteristic of the Sheikah) and has some magical power, one of which being the ability to erect a barrier of light to defend against Yuga- a power also demonstrated by Impa in SS. Assuming these similarities aren't just coincidence (which is always admittedly possible), these imply some connection between Hilda (and with her the Loruleans) and the Sheikah.
With this in mind, here's my idea. Lorule's Triforce was originally destroyed to end the fighting over it. However, it is doubtful that it could be physically destroyed- the Hyrulean Triforce could seemingly be broken into infinite fragments without ill effect (as separating it into parts, then shattering those parts, did not cause Hyrule to begin crumbling). Hilda also says that it was destroyed "utterly and absolutely", ultimately requiring a wish on Hyrule's Triforce to restore it. This, again, implies no physical remains. The only known way this could occur would be if the Triforce itself was used to wish for its own destruction. Hilda claims that her ancestors destroyed it, meaning one of them must have made the wish. But who? Well, Hilda is the parallel counterpart of Zelda, and both princesses display magical power. The latter's powers came from the blood of the goddess Hylia; it would be logical, then, to assume that Hilda received her powers from a divine bloodline as well- that of Hylia's Lorulean counterpart, who I call "Lylia". SS, however, establishes that gods are unable to use the Triforce; Lylia, then, must have given up her divinity to destroy it. Afterward, she founded what would become Lorule's Royal Family.
After this, Demise then crossed from Lorule to Hyrule (as discussed in other threads here, and elsewhere as well) to take its Triforce. Knowing that this would lead to, or at least worsen, fighting over the Triforce, and perhaps even drive Hylia to the same desperate act, some of Lylia's mortal children followed Demise into Hyrule using enchanted bracelets (one of, if not the, last of which eventually coming into Ravio's, then Link's possession). After helping to seal Demise, these Lorulean demigods decided to make sure that Hyrule was never at risk of losing its Triforce, and so, they swore fealty to Hylia, becoming her servants and protectors- the Sheikah.
Thoughts?
With this in mind, here's my idea. Lorule's Triforce was originally destroyed to end the fighting over it. However, it is doubtful that it could be physically destroyed- the Hyrulean Triforce could seemingly be broken into infinite fragments without ill effect (as separating it into parts, then shattering those parts, did not cause Hyrule to begin crumbling). Hilda also says that it was destroyed "utterly and absolutely", ultimately requiring a wish on Hyrule's Triforce to restore it. This, again, implies no physical remains. The only known way this could occur would be if the Triforce itself was used to wish for its own destruction. Hilda claims that her ancestors destroyed it, meaning one of them must have made the wish. But who? Well, Hilda is the parallel counterpart of Zelda, and both princesses display magical power. The latter's powers came from the blood of the goddess Hylia; it would be logical, then, to assume that Hilda received her powers from a divine bloodline as well- that of Hylia's Lorulean counterpart, who I call "Lylia". SS, however, establishes that gods are unable to use the Triforce; Lylia, then, must have given up her divinity to destroy it. Afterward, she founded what would become Lorule's Royal Family.
After this, Demise then crossed from Lorule to Hyrule (as discussed in other threads here, and elsewhere as well) to take its Triforce. Knowing that this would lead to, or at least worsen, fighting over the Triforce, and perhaps even drive Hylia to the same desperate act, some of Lylia's mortal children followed Demise into Hyrule using enchanted bracelets (one of, if not the, last of which eventually coming into Ravio's, then Link's possession). After helping to seal Demise, these Lorulean demigods decided to make sure that Hyrule was never at risk of losing its Triforce, and so, they swore fealty to Hylia, becoming her servants and protectors- the Sheikah.
Thoughts?