Death With Interruptions — Jose Saramago

On the first day of the new year, no one dies. This of course causes consternation among politicians, religious leaders, morticians, and doctors. Among the general public, on the other hand, there is initially celebration--flags are hung out on balconies, people dance in the streets. They have achieved the great goal of humanity: eternal life. Then reality hits home--families are left to care for the permanently dying, life-insurance policies become meaningless, and funeral parlors are reduced to arranging burials for pet dogs, cats, hamsters, and parrots.

Death sits in her chilly apartment, where she lives alone with scythe and filing cabinets, and contemplates her experiment: What if no one ever died again? What if she, death with a small d, became human and were to fall in love?