This should free up the shape file for purging if it was referenced in a linetype. Set all layers to use the Continuous linetype, and make sure all entities are set to Bylayer linetype. Purge all linetypes and then see if the shape file can be purged.
If you want to remove the SHX file references forever, you will need to purge them from the drawing. In any case, AutoCAD cannot find the shape file. If you do not have it, then perhaps you received this drawing from someone else? What if this is an internal drawing that you have been working on for a while? Most likely though, they are part of a complex linetype definition. Shape files contain shapes that can be used by themselves, sort of like blocks.
If you receive this dialog, it means you are missing a shape file that is referenced in the drawing.
Author: rkmcswain November 4, A very common issue with AutoCAD is the presence of the dialog below.