Ask Mr. Smarty Plants

If we understand you correctly, you are looking for a way to propagate your Yucca treculeana (Don Quixote's lace) because you need to remove the one you have from a space where it has become dangerous to passers-by.  We could find no evidence that it reproduced by contact of the trunk with the soil, although there are plants that do that. It would appear to us that you do, indeed, need to modify that particular plant, which isn't going to be easy, but necessary. First, though, you can take cuttings from the plant and root them, to be replanted in another location not so near a walkway. This website from Gardening Know How Propagation of a Yucca Plant gives good instructions. Apparently, this is the right time to do so, as these cuttings should be taken in the Spring.

From the same source, this website is on Pruning a Yucca which involves cutting the trunk off at some point, and leaving it in place to resprout leaves. From Fine Gardening, yet another article on Propagating Yucca.

After reading all these, our advice is to prune that yucca by cutting through the trunk about halfway up. Then, you will need to repeat the process every year or two, to keep it from getting so big and out of hand again. The trunk is very fibrous and not easy to cut, but it can be done. New growth will begin to sprout in a short time. In terms of avoiding the prickly tips as you prune, we suggest you mark the point at which you are going to cut through the trunk, and cut back everything above that (and even a little below) so you won't be dealing with those spines as you cut the trunk. For this, you will need long pruning shears, and wear long sleeves and pants, leather gloves and a pair of goggles to protect your eyes. By using this technique, you won't have to try to dig up the old plant (really hard!), nor take cuttings to make new plants. Be careful how you discard the trimmed-off portions, they will poke right through a plastic trash bag, but you can find heavy duty paper trash bags that should suffice. And don't try them in a compost pile-it takes them a long time to decompose, and they maintain their stickeriness throughout.  

From our Native Plant Image Gallery:

Yucca treculeana

Yucca treculeana

Yucca treculeana

Yucca treculeana