When Edge Softening fails to produce a closed mesh, all faces become unwelded, therefore it makes further actions on mesh very difficult/impossible.
FWIW edge softening is intended to be used as a visual gimmick at best, and won’t work with for instance big radii in many cases. If you need softened edges you should fillet them instead so you keep control.
Visual gimmick is all what I need in this case. 
I want to use those render meshes inside game engines etc. Filleting would be a huge overkill.
Can you share the mesh from the video?