My garden nemesis is Campanula rapunculoides. Many years ago, someone thought it would make a nice garden plant, and now it is throughout our lawn, and regularly appears in our new gardens, sprouting from tuberous roots that may be up to 40 cm below the surface of the soil. Whenever one shows above ground growth, I get out the fork, and do my best to find the parent root and remove it. It is shocking to see some of the plants that are still being sold as perennials/groundcover or perennial seed in the nursery trade (Campanula rapunculoides is just marginally better than Aegopodium podagraria... I've seen both offered as seed or potted plants).
Southwest Nova Scotia, zone 6b or thereabouts
I consider it shocking as well! This is a horrible weed everywhere. It's escaped from gardens into natural areas here.
Yes, finding the "parent root" - the white, carrot-like, vertical root that's usually several inches or a foot or more down into the soil - seems to be the key to fighting it. Pulling out the thready roots that join plants in the colony has no effect. I've kept it out of my yard that way (by digging out the white basal root), though my neighbor has an infestation. The really sad thing is that people willingly introduce it to their yards!!
Calgary, Alberta, Canada - Zone 3
-30 C to +30 C (rarely!); elevation ~1130m; annual precipitation ~40 cm