A world like this exists in a book called 'They Both Die At The End'. People are called by a company called Death-Cast that calls them the day of their death to tell them they're, well y'know, gonna die. They can't say how or why though, so imagine living your last day with constant anticipation of the end, not even knowing what will happen to you but knowing that your end is drawing near
Shin Megami Tensei Devil Survivor 1 and 2 had both a similar premise. In 1, people would see other people's "death clocks" which stated how many days they have left, and in 2, you could subscribe to a website which would send you videos of your friends' deaths right before they'd die.