For my iOS application, what event will be triggered when user a is about to delete the application?
I'm afraid that there is no such notification. When your apps isn't running there's no way it can be notified of changes!
Instead you need to save any state when your user presses the home button, i.e., when it "resigns active." (There's a callback in the UIApplicationDelegate and you can also listen for notifications.) In general I would not recommend listening for UIApplicationWillTerminateNotification since it is rarely called on iOS4 where multi-tasking is supported.