Why doesn’t stopping an application in iOS simulator trigger applicationWillTerminate:?

The simulator doesn't send applicationWillTerminate: because the springboard isn't sending you the kill code (SIGABRT), LLDB is. To trigger those delegate methods, you have to use the Home Button command (⌘+⇧+H), then pull up the multitasking drawer and kill your application from there. Your debugging session will immediately terminate, and the delegate method will fire successfully.