Why'd Sharkey do that?

[Eomer of the Rohirrim]

Maybe it's not so much that he wanted to die, but I don't think he wanted to continue his miserable life. If he did want to survive and go somewhere else then he would have left as soon as Frodo returned and he would not have tried to murder him. He was basically asking for the Hobbits to kill him by killing Frodo.

And there's that metaphor of the sighing spirit being turned away by the Western wind (metaphor? It might be...) It suggests that Saruman thought the whole affair pathetic and 'sigh-worthy'.