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.
Prepare for It. This one is easy. All you have to do is smile and say "Thank you so much for your support. I've enjoyed my time here and I've learned a lot from you. Let me know what I can do to make the transition easier." Are you always going to get reaction number five? Probably not. But if you look for the signs, you can likely anticipate your boss' response, go into the conversation prepared, and come out stronger on the other side. Then, you can breathe a sign of relief and start looking forward to starting your new position.