An idea from a visual novel video game I recently played:
Recently, the God of Death has had a soul-shaking experience that has left them now longer willing to cull the living. This manifests during the party's next encounter (which should start out as fairly minor), when after reducing foes to 0 hit points, they don't die (that also happens to go for PCs...). Regardless of the amount of damage, the undying's body gain a bit of supernatural resistance so that short of special effects like Disintegrate (which just turns the poor victim into a ghost), no one can any longer die and the body is fairly indestructible (though those at 0 hit points become ravening killers hateful of those alive). The two sides will need to find a cunning way to end the fight. Note - returning an individual to 1 or more hit points removes the undying status, though each time permanently reduces max hit points; some sort of nasty side effect if max hit points drops to 0 (unconscious? incapacitated?)
Thereafter, after a couple more similar incidents (fights, encountering an individual who is unable to end their suffering and move on to the afterlife, witnessing an accident that >should< have killed the individual or even someone begging the PCs to return someone from death now that Death seems to sidestep their "duty") and a long rest, a cabal of the other gods contact the party, with a proposition - visit Death, convince them to return to culling the dead or slay them and replace them. The gods cannot perform this task themselves because it is beyond their sphere of influence, Death has denied them access to the underworld and they really don't want to risk being the target of opportunity if/when Death decides to pick up their old habits of culling individuals.
Of course, before visiting the House of the Dead, the gods have three trials to put the PCs through. These are both to see if the party is up to the task, as well as grant them boons/items to help them in the next part of their quest.
(Don't have ideas at this time for the trials, or the specific items/boons)
After completing the trials, the PCs must make their way to the underworld, which may be aided by the gods. The trip shunts the PCs into a labyrinth section of Death's house, as of course they don't like unwelcome visitors. After running the gauntlet, the party eventually comes to Death's den. The PCs then need to persuade, cajole, threaten(!?!), or otherwise convince Death to take up their duties - or dethrone Death and take their place. One of the most extreme options may be to enrage Death to the point they kill a character, restarting the cycle. Once their task is complete, the party needs to find a way back - Death does not so easily relinquish visitors to their realm.
POSSIBLE OPTIONAL COMPLICATIONS
- The God of Life/Rebirth's hand is stayed until Death resumes their tasks. No new life can be created; offspring cannot be conceived nor birthed until Death resumes their task.
- Food sources become scarce as animals cannot be slaughtered, crops resist harvesting and the like.
- One of the cabal of gods wants to use the PC to rig Death's future cullings so a disproportionate number of souls are directed to them, increasing their power.
- The gods have a backup plan and have tapped a rival group to complete the task if the party isn't up to it. The rivals might even be formal nemesis of the party. (This could get really complicated if the PCs don't want to stop Death themselves and decide they want to become undying).
- Those who cannot die are prone to rampage; between trials the PCs need to intercede in various events of the undying being out of control
- A simple Orc or other raiding force's attack is complicated when the village they raid can't die. The orcs can't die either, but they're stronger and can make the unfortunate (undying) villager's lives a living hell. Furthermore, once Death resumes their task, all the undying villagers will die for good...
- A demagogue-led cult preaches the benefits of becoming undying, converting believers via ritual suicide (or slaughter) and targets the PCs to stop them from completing their task.