Underground running roots can develop suckers as they grow beyond the shade of the mother clump. These suckers can be cut away from the main plant, or you can dig up the main plant and cut away any piece with an eye or sucker already forming.
Plants with underground running roots: hardy geraniums (Geranium spp. and cvs., Z 4–9), Japanese anemones (Anemone × hybrida cvs., Z 4–8), ostrich fern (Matteuccia pennsylvanica, Z 3–8), plume poppies (Macleaya spp. and cvs., Z 4–9)
In this video, author and instructor Janet Macunovich demonstrates how to divide perennials with underground running roots.