We determined that the slug was not stored in postmeta meta_key _wp_old_slug.
In a final attempt to find where this slug is stored. I performed a search for the exact phrase of writing and found a few results. The one of interest was in wp_terms.
I deleted that entry and then changed the slug of the category to /writing and it is working. The strange part was that there were no records within wp_terms that connected the post to the slug.