[Galadriel55]

And there's no one more fit that Turin to carry out the prophecy! I think that out of all the thousands of Elves, Men, and Dwarves whose lives Morgoth ruined, Turin's was by far the worst and most bitter (Unless it be Hurin, but as Puddleglum rightly said, Hurin did not want to stay any longer in the world). Turin wanted to strike the final blow to get revenge on Morgoth. He was trying to do that all his life, but because of the curse all his efforts somehow turned on himself. Imagine it like this: Morgoth punches Turin; Turin wants to punch him back, but ends up punching himself. When he realises that he hit his own face, he punches again, and again hurts himself... This way Morgoth can leave the family to their own devices, and they'll be destroyed by, basically, themselves.
To answer Urwen's question as to why Morgoth "cursed them to death", it's probably because he was enraged about Hurin's mockery. He didn't kill him, didn't make him work, but made him suffer inside. Does he really care about 3 innocent individuals? He's MORGOTH, he doesn't give a hoot in hell about one little family. He destroyed thousands of families, but Hurin's got special treatment, since Hurin opposed Morgoth more than the others. And he didn't curse them to DEATH - that would be stupid of him. His curse caused their death, but it had better results when they were alive, preferably doing something big scale.