You have to be interesting before you can be made sympathetic

If you need to introduce a character that will later be killed off or suffer some tragedy, make sure that you make them interesting first. People won't be as connected to a generic character. E.g. TV show Bitten - they introduce a woman who will later be killed; her story is just that she's a young bride about to be married, and is related to the main character. There's not enough there to really hook the reader in - we can see what's coming, we can predict this character will be gotten rid of. If she seemed more important to the story, it would have more impact when she was taken away, with the greater purpose of creating a sense of unpredictability for the reader.