Freestyle > Adding Detail to the Control Mesh > Resolving Doublets
  
Resolving Doublets
When you add or delete edges, some vertices may remain connected to only two edges. These vertices are called doublet vertices or doublets.
By default, the Auto delete doublets check box in the Freestyle Options dialog box is selected and the doublets are automatically deleted. However, if you clear this check box to retain the doublets, the system prompts you to manually resolve the doublets to complete the Freestyle feature. Click Operations > Options to open the Freestyle Options dialog box. You can add edges, delete the doublet vertices, or extrude, split, or join the faces to resolve the doublet failures.
Alternatively, you can set the configuration option auto_del_doublets to no if you do not want to delete doublets automatically.