Then the date would have to be re-calculated because knowing this new date could cause the date to change in a different way, requiring another recalculation, etc. I guess it really depends in practice, might only be a few loops before it gets stuck on one date, could see it being an infinite loop though
Rick and Morty did something similar in the episode "Edge of Tomorty: Rick Die Rickpeat". Morty got ahold of a crystal that showed him what his final moments would look like, and the vision updated as his actions changed his future.
If the letter told me the exact date and time of my own death, I might go crazy, though.