The Zero weighted Operator selects all vertices for which the sum of all assigned weights is 0.0 (zero).
Note: this operator does not preserve the original vertex selection. So after the operator is called, only the zero weighted vertices are selected or no vertex is selected when the mesh is clean (all vertices have weightsums > 0)
Note: When you have selected multiple Objects you will find a report in the Blender Console with one line per object indicating the number of vertices with weight sums == 0
How to fix
You fix this in the same way as you handle unweighted vertices, see above.