The guy from The Crow was Brandon Lee...they kept all of his scenes, and maybe they even did a little tribute at the end. I know that right before River Phoenix died, he had been selected for Interview with the Vampire, and he hadn't done the scenes. Christian Slater ended up doing them, and they memorialized River in the credits.
I guess this is similar to TV shows/movies editing out scenes of the WTC...some people approve, while others don't.