New shoots may grow from the base of your yucca that was left when the trunk was removed. If this occurs you could dig out the crown to keep it from producing more shoots.
It is also possible that new shoots may grow from large roots in the ground. To live and grow, roots need sugars and other compounds produced by plant leaves. Roots may survive for a while on starch stored in woody tissue, but they will eventually die if there are no leaves to nourish them. The roots of your Yucca will stop growing and eventually die if you promptly remove any shoots that grow from the base of the trunk or large roots.
The re-growth of sprouts can be prevented by treating the trunk with an herbicide such as triclopyr (Ortho Brush-B-Gon) or glyphosate (Roundup). Use a sharp axe to cut through the bark at a 45 degree angle around the base of the trunk to create an open flap with a small reservoir. Apply herbicide to the fresh cuts immediately. A stump or root can also be treated by making a new cut across the end to expose fresh tissue. Immediately apply the herbicide to the outer portion of wood and bark.
For more information, see UC Pest Note 74142 – Woody Weed Invaders. http://www.ipm.ucdavis.edu/PMG/PESTNOTES/pn74142.html
By V. Lazaneo, Urban Horticulture Advisor, Emeritus, UC Cooperative Extension,