At the end of episode 6 she appears next to her tomb and both main characters seem to see her. So either there really are ghosts in SAO or she was alive, and if she was alive, why didn't she appear anywhere else later, etc? The story was left open so ambiguously that now my brain is bleeding.
Quote from the 8th volume of the Sword Art Online Light Novel (translation from baka-tsuki):
Shocked, I turn to look behind, and what was in front of my eyes——
[...] it's impossible for supernatural phenomenon to happen.
So is this a bug in the server I see? Or is it an illusion in my breath?
Not far away, [...] there...was a translucent female player giving off a slightly golden light.
[...] However, after a while, she extends her right hand over to us to seemingly hand something over.
Asuna and I reached our right hands out, and as we felt the warmth, we clasped onto it tightly. This warmth entered our bodies, lighting the fire within our chest. We opened our mouths and said out the words the form within us.
Asuna's words rode through the night wind and reached the female swordsman. The transparent face showed a large smile——
And in that instant, nobody was there.
We put our hands down and remained spaced out over there for quite some time.
It was described pretty clear that Grimlock killed Griselda. Why she was still visible wasn't explained, but because she disappeared without a trace, it was most likely just an illusion or some kind of hidden feature. She's definitively dead ;).
It's something similar to when Kirito died against Kayaba and came back to life. It's the incarnate system, something that was added into the game but nobody was aware of it, only becoming more of a common knowledge in Accel World. Even then, only a few people know of it.
In the novels of SAO, it's being mentioned, since it's a soul dive that's being used, not the mind. It's the manifestation of the will, to make them stronger. Kayaba's idea, that was fully completed later on.