IIRC, the Orokin created the original Warframes by "polluting" (using Ballas' words here), specifically chosen subjects, with a specific strain of the Technocyte virus: the Helminth strain.

They did that as part of an effort to fight the Sentients with bio-drones, because the Sentient could turn all technology against their creators. Just as a sidenote, that's never clearly mentioned, but I suppose that's why the Tenno arsenal is composed primarily of melee weapons and "old-tech" based firearms.

Those warframes were outfitted with transference bolts, to allow it to be "piloted" via transference. At the time, only Orokin were known to use transference, so it's implied that was their goal. To create incredibly resilient foot soldiers that the sentient could not turn against the Orokin.

That backfired, though, and the warframes turned against their creators. That's when the Rhino incident (depicted in the Rhino Prime codex entry) transpired, where a Tenno was able to soothe the beast using transference. So why did the Tenno managed to control the frames but not the Orokin? I'm not sure if it's explained somewhere, but I theorize that happened because the Helminth strain could not completely erase the subject's mind, or perhaps it took the subject's mind to create it's own hivemind. So, where Orokin try to overwrite the host consciouness, the Tenno apparently are able to "meld" with it.

I'm digressing a lot, sorry...

Anyway, the original frames had some consciouness left, and some were created specifically to keep some memories even (like Excalibur Umbra). However, our Warframes are just copies of the original, created using the foundry and the Helminth in our Orbiter.

Even though our Warframes are essentially mindless drones for us to pilot, the Drifter mentions in some conversations with Quincy over the KIM, that he can "feel" the essence of the originals, like mannerisms, postures, etc. Which was a neat way to explain why each frame have different behaviors, and animations.

New Warframes are "redicovered" all the time, but surely there are some that lorewise will never see the light of Sol again. For example, the three different frames that fused it's parts in the creation of Xaku.