Immortality as a form of punishment or torture

Prometheus (Greek Mythology) - for bringing divine fire to common humans, he was chained to a mountain and had his liver eaten by an eagle. Unfortunately, he could endure this more than once after being "blessed" with immortality and a healing factor.

Quynh (The Old Guard) - Burned at the stake for witchcraft. When she survived that, they put her in an iron coffin and sank her to the bottom of the Atlantic Ocean.

The Black Pearl crew (Pirates of the Caribbean) - Stealing accursed Aztec treasure let them live without the need for food or water. Unfortunately, they can no longer eat or drink, but they still feel ravenous hunger and desperate thirst.