Socketing a damaged armor/helm and then improving its quality (with the “El Rune + chipped gem” cube recipe) removes the sockets.
I found threads on the internet asking the question but haven’t found an answer so I sacrificed a socketing quest to find it out. (The socketing was done by a character that was rushed through normal difficulty specifically for the socketing quest.)
I used a “Damaged Bone Visage” that received 3 sockets from Larzuk. After socketing the name was still “Damaged Bone Visage” and the cube recipe (El rune + chipped) worked with it but removed the sockets. To make it worse, the defense barely improved: it was ninety-something (don’t remember the exact value) and the improved defense is 108. (Can this cube recipe roll max defense?)
The recipe sets the ilvl to 1 so using it before socketing would give only 2 sockets with a Bone Visage:
http://classic.battle.net/diablo2exp/items/cube.shtml
https://diablo2.diablowiki.net/Sockets