No I do no think the roots is what makes the plant look dead. I think it maybe that they sulk and that is their way of showing they are sulking and the tops die back and the new growth from the roots is what makes the tall sticks.
If you think about it perennials plants die down to the ground and grow back when Spring arrives. When they are happy they grow new sticks when they feel they are secure enough in their new growing conditions. I just would not pull the plants out until you are sure the plant is really dead..
