In Anime trailers

[Bob Schroeck]

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Tetsusaiga as a Remnant? How do those work, anyway?

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A Remnant is a Celestial who has lost all his Celestial Forces (out of the triad of Corporeal, Ethereal and Celestial). This leaves him with intellect and physical presence, but all his connection to Heaven (or Hell) is lost, and usually so is most of his memory of being anything other than a corporeal being. They lose a lot of themselves with those Celestial forces.
I believe Gryphon once described Rei in NXE as a Remnant, albeit one who has -- despite all odds -- managed to heal herself. (Theoretically this is possible in the game, too -- if the Remnant can earn enough experience to buy new Celestial Forces. Or a Superior can graft on new Celestial Forces. But the result is never the same as the being who originally existed.)

-- Bob
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Then the horns kicked in...
...and my shoes began to squeak.