I have an unusual plant growing in the Garden that comes up again 3 days after I pick it out. The root system is complex and very thick about 1 inch in diameter and 1 foot under the soil. What grows seems almost akin to leaves of horseraddish but surely you don't dig down that deep to farm horseraddish roots. Oh yes small white flowers grow on stalks in the spring and all the leaves grow on stalks from the base. Snails love it for shelter and its engulfing my newly (spring) planted flowers.
Try putting some ordinary kitchen salt over the roots, be careful not to touch the roots of any other plants with the salt. . If you can, pour boiling water over the salt, again without spreading on other plants. Keep putting salt on until the the weed dies.
Hi monkey, This sounds like Bishops Weed otherwise known as Ground Elder. This is a B........ to get rid of. You virtually have to get down on hands and knees and dig is out making sure you remove all of the fleshy roots as even if you leave a tiny bit it will grow. I have quite a lot in my garden and am only able to keep it in check by continually removing new growths as they appear. Best of luck Skylight