Hi: The attached image was taken of a plant that has shown up in and around my vegetable garden. I've pulled about a dozen of these plants out of the ground, but in a few weeks they just grow back. They would never get too tall since I mow on a weekly basis. I'm speculating that some animal ate something and deposited the seeds. Assuming it's some sort of perennial.
I agree with Daniel... Compare with Asclepias syriaca. They have a vigorous system of rhizomes. http://thecluelessgardeners.blogspot.com/2010/08/milkweed-roots.html But... it's so valuable for the disappearing monarchs... Consider encouraging the milkweeds rather than the turf...