Spot the Signs. You may receive this reaction if you're a high_ranking executive or director. These positions can be difficult to replace quickly, so it may be worth it to your company to tempt you to stay rather than letting you go without a fight. It can also happen if you have extremely specialized knowledge that would make it challenging to replace you. On the other hand, if you're in an entry_ or mid_level position, and someone could be hired into your position without much trouble, it's less likely your boss will put up a fight__and a counteroffer.
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.