someone who dies on their birthday

If I needed such a term, I would use "someone who died on their birthday". (The generic singular use of they did not even give me pause to wonder.) If something more exotic, ad hoc, and nonce-like is desired, one could read some biographies of people who died on the same day they were born. Collection of a list of such people would be a necessary prerequisite.

Ceci n'est pas un seing.