In object mode there is a blender element attached to a particular object which appears to be a vertex, though I'm working in a large scale, so it could be a small edge or face. I don't want it there, but I cannot seem to select the item in object mode, and it disappears in edit mode.
A hard to find or select object can often be deleted from the outliner.
Here I have a cube that has all of it's vertices deleted but is still a child of another cube. In the outliner I can expand the parent to see the child, by right clicking on Cube.001 I can then select delete.