As far as I know you really can't do that.
"If I remove objects form a group that group still exists without objects"
Actually he group doesn't really exist anymore. It's name is listed because the datablock hasn't been erased yet. If you save your file close blender and reopen the Group name will be gone.
Only thing you can do is select all the objects you want to add to the "ghost" group (make sure you click at least one of them to make it active), add one via the menu in Properties Window > Object > Groups > Add to Group, then with the cursor hovering the 3D View press Ctrl + L > Link > Group.
Have in mind though, that if any of the other objects already belonged to any groups previously they will be removed from them to match the active object's.