The Hand_off. Finally, state your willingness to help out with the transition. You don't need to go into great detail (and definitely don't promise anything you can't deliver), but a couple of lines stating that you'll ensure a smooth wrap_up of your duties will show that you're in the game until the very end. Obviously, feel free to adjust this a bit based on your experience and your company culture, then submit it via the typical procedures at your company.
Asking You to Stay Beyond Your Notice. In this situation, you won't necessarily get the promise of more money or a better title__but your manager will ask you, perhaps as a personal favor, to stay a few additional weeks or months until the company is able to hire and train a replacement.