John B
"With or without religion, you would have good people doing good things and evil people doing evil things. But for good people to do evil things, that takes religion." - Steven Weinberg.
It was obvious from the original post that we are dealing with a shape file, not a font file. The only way to get prompted about a missing font file, is if you do not have a FONTMAP file, and FONTALT is set to nothing. If these conditions are true, then you get the dialog shown below:
Notice the dialog is not asking for a specific "SHX" file, it's only asking for a font name from the list of fonts (either .shx in the support file search path, or .TTF as installed in Windows)
When there is a missing shape file, you are prompted with a standard Windows file selection dialog, to select the actual SHX file that is missing. This is what the original message said.
A little late, but here it is if you need it.
To clarify, it is indeed a complex linetype Shapefile.