. . . . What element uses highslide.css files . . . .
It is an image, media and gallery viewer called Highslide.
Which 'dead link' checker are you using?
If for example you are using the Google Search Console then if the search bots ie Googlebot see a robots.txt file which prevent it from scanning parts of the site then it may return a 404 error for files it cannot reach.
Check in the sites index_htm_files folder that the highslide.cssdoes exist.
Has an image gallery been removed from a page(s), or moved to another page?