whether you wake or sleep, you will live with him
It seems Dr. Piper is equating sleeping, here, with death, and implying that we needn't fear death because it's not real.
I used to fear death, when I believed there was an afterlife and I was plagued with doubts about whether I would be playing the harp in the clouds, or suffering eternal torture. Once I realized there isn't anything after death, I was able to understand that dying is just like not being born yet. I've already experienced that.
The only fear left, really, is the fear of a painful death. But, I have a fear of painful life, too, so I have to keep dealing with that one.