Death at Intervals

In an unnamed country, on the first day of the New Year, people stop dying. There is great celebration and people dance in the streets. They have achieved the great goal of humanity: eternal life. Soon, though, the residents begin to suffer. Undertakers face bankruptcy, the church is forced to reinvent its doctrine, and local 'maphia' smuggle those on the brink of death over the border where they can expire naturally.
Death does return eventually, but with a new, courteous approach - delivering violet warning letters to her victims. But what can death do when a letter is unexpectedly returned?