This is what I had learned, though I've been paying particular attention to grammatical coloring as I read lately, and I've noticed the use of the semicolon by some authors following an independent clause and preceding a fragment.
I cannot reconcile this with any proper rules, yet there is lies on the page. I personally find it very fitting. I often have a sentence fragment that is an afterthought of a previous sentence where I would personally find it very befitting to add a semicolon to tie the ideas together without creating a whole new sentence or independent clause to add the secondary idea.