Spot the Signs. According to Alison Green, who writes the blog Ask a Manager, this is common practice for some industries, especially if you're leaving to work for a direct competitor. However, in those situations, you'll likely know it's coming and can prepare accordingly.
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.