Nut, some pennisetums are invasive. I split them every year for this very reason and this keeps them floriferous and compact. I learned this lesson few years back when I had to dig up pennisetum villosum that had grown large. It was a difficult job as the roots had spread everywhere...deep and laterally. You are right, their "live parts are well down" , esp on plants that have been in place for more than a couple of years. They do very well in pots hidden amongst other plants making beautiful mounds of flowers but without their invasiveness
