If consciousness stops and restarts, how would you ever know?

When we wake from sleep or anesthesia, it usually doesn’t feel like we experienced a gap. It feels more like: I was there, and now I’m here. But from the outside, there was clearly a period where normal conscious experience was absent.

So if consciousness actually stopped and restarted, would the subject ever be able to detect that?

Or would the restarted mind simply feel continuous because it inherits memory and narrative continuity?