When Jesus said "It is finished" on the cross, He gave up the "ghost". I think that's a very overlooked part of scripture. It's consistent with our spirit and or soul leaving our fleshly body in the invisible realm where angels and demons reside.
In the movie Sixth Sense, we find out in the end that Bruce Willis's character has been dead the whole time. He thought his wife was ignoring him. If you get the chance, read George Ritchie's NDE claiming the same thing.
This link is the atheist's NDE.
Steve M