Marilyn Monroe while starting Something's Got to Give with Dean Martin and Walter Mattau. The film was scrapped.
Oliver Reed during Gladiator, although it was said that most of his scenes had been finished.
It is rumored that Orson Welles died during voice work for the Transformers movie and Leonard Nimoy finished his scenes with voice modulation. Although, by most accounts all of his tracks were laid down by the time he died.
Got to go to work or I would think of more. Usually in these cases another actor is cast if it's early enough in the filming or the movie is edited around them. Sometimes you do wind up with the project getting scrapped.