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.
Otherwise, look to the history of your company. How have your boss and other managers handled employees' resignations? If you see a pattern of upper management refusing to let the team members work out their notice, you can likely expect the same.