I was climbing SRT, trunk tied the other day and was thinking about something coming loose at the anchor, be it, a groundie cutting the rope, whatever.
The major issue I see is that if the 'event' happens while you're ascending, i.e. you are hanging solely from the rope when the anchor/rope fails, you'd fall. It's that simple.
It occurred to me that I could 'trail' a Petzl Shunt on the anchor side of the rope (the Shunt tied to my harness of course). If the rope or anchor failed below the Shunt, the Shunt would arrest the fall. Well unless a rope failure occurred so close to the Shunt that the Shunt couldn't grab.
One caveat I see to this is that you'd pretty much have to have the rope isolated on one limb, or move the Shunt over a limb as you got to it. Another is the climbing side and anchor side of the rope would need to be moderately close to one another.