I have found references to birthdays and "deathdays," many words that reference either death or birth (natalis, obitus, quietus) but not both sharing the same day and month (even sharing the same year in the case of some children).
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To my knowledge, it is "neonatal death". It is used to imply the death of newborn baby in first 28 days.
A person who died on his birthday is described as "birthday-perisher"
There is one expression that might be suitable for this case and it's stillbirth. Stillbirth is often defined as fetal death after 20 weeks of gestation,but a fetus greater than any combination of 16 to 28 weeks gestational age.