Thank you all for your feedback. The scale does help the result. The fragment is the edge of a Roman tomb, so the edge was rather small. However, when changing the scale, there are still some flaws in the resulted skin. I don't think it has to do with hidden geometry being an obstacle. Any ideas?
Dave R, yes, ,you are correct that the 'follow me' function would be a solution. Yet, I had not used this plugin before, and just liked to see its possibilities.