This optional scene underwent more than just cosmetic augmentation between the Original and Remake. This scene is triggered if the player - Chris Redfield - does not save Rebecca from the Hunter in time.
Chris hears a scream while he is searching in Spencer's office. Rebecca is shown in the study near the staircase, with the door broken and forced into the corner of the room by a Hunter. Chris may or may not get to the room in time, but the creature can still kill Rebecca. Her throat is sliced and she dies. This time, Chris merely falls to his knees in despair and mumbles "No...".