Thrift is a lovely perennial that thrives in good drainage, full sun and can even tolerate salty air near the seaside. The roots you describe emerging are because the plants are now mature enought to be divided. Wait until fall or early spring. Uproot a clump and pull apart the sections discarding the oldest or middle part of the plant if the roots look dry. The side shoots can then be replanted and watered well after the transplant. Do not fertilize after the transplant. This plant flowers best in full sun with little to no fertilizer. I suspect you will have plenty of baby thrift plants to spread around your property or to share with friends. Enjoy! Keep growing, Marianne Binetti