Reverse chronology — narrating a story, or parts of one, backwards in time — is a venerable technique in literature, going back at least as far as Virgil’s Aeneid. Much more interesting is a story with incompatible arrows of time: some characters live “backwards” while others experience life normally.
Probably the most famous contemporary example is Martin Amis’s chilling novel, Time’s Arrow.
Eating is unattractive too… Various items get gulped into my mouth, and after skillful massage with tongue and teeth I transfer them to the plate for additional sculpture with knife and fork and spoon. That bit’s quite therapeutic at least, unless you’re having soup or something, which can be a real sentence. Next you face the laborious business of cooling, of reassembly, of storage, before the return of these foodstuffs to the Superette, where, admittedly, I am promptly and generously reimbursed for my pains. Then you tool down the aisles, with trolley or basket, returning each can and packet to its rightful place.
The narrator of Time’s Arrow is a disembodied consciousness who lives inside another person, Odilo Unverdorben. The host lives life in the ordinary sense, forward in time, but the homunculus narrator experiences everything backwards – his first memory is Unverdorben’s death (although, for expository purposes, he comes into existence as a full, speaking intellect). He has no control over Unverdorben’s actions, nor access to his memories, but passively travels through life in reverse order. At first Unverdorben (going under the name of “Tod Friendly”) appears to us as a doctor, which seems like a morbid occupation – patients shuffle into the emergency room, where the doctors suck medicines out of their bodies and rip off their bandages, sending them out into the night bleeding and screaming. But near the end of the book, we learn that Unverdorben was an assistant at Auschwitz, where he created life where none had been before – turning chemicals and electricity and corpses into living persons. Only now, thinks the narrator, does the world finally make sense.