In the Middle Ages, and even up to the early twentieth century, most of Europe's executioners were related: the Sansons and Deiblers in France, the Pierrepoints in England, etc. The reason for this was that, it generally not being socially acceptable to, well, kill people, executioners and their children could, generally, only marry other executioners or their children.
The parallels with massively inbred, Hapsburg-style dynasties are obvious- imagine a rather clever but politically inept satirist noting this, and being sentenced by the latter to a meeting with the former; even worse, imagine a dynasty of deranged and deformed executioners- think Texas Chaisaw Massacre with government funding.
Minor Cultural Modifier: The culture believes, for the soul to leave the body, the corpse' eyes must be open. So any member of that culture takes care any dead body they find has its eyes open. Doubly true for those they kill themselves, for then the corpse will surely rise as an undead hunting him.