In this performance, they sing, "will the circle be unbroken?" The song was originally "Can the Circle Be Unbroken?" when it was first recorded by the Carter Family in 1935. They had a hit with it in the summer of that year. You can listen to the original version here.
"Will the Circle Be Unbroken?" is a hymn from 1907 with words by Ada Habershon and music by the great Methodist hymn writer Charles H. Gabriel. If there were a decent recording of it on Youtube, I would supply a link.
The two songs are often confused.
Thanks, Fiji...somewhere on my hard drive I have some old Carter Family stuff. I have that album. Gonna have to look for it.
Happy Thanksgiving.