Our consciousness does not even survive falling asleep at night, it is that ephemeral, goodness knows how anyone could think it could survive the catastrophic cellular breakdown of death.
As far as I am aware, no one has actually come-up with a satisfactory definition of what 'consciousness' is!
We feel it, we know it, we ARE it - but what is it?
Certainly, the brain appears to be central, it connects 'us' to the material world, so no big surprise that 'we' are not present when the brain 'shuts down'.
If I were to do some theology/cosmology 'on the fly' I might hypothesis that a part of us consists as a 'clump of dark matter' that becomes attached to living things.