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.
However, at most companies, there's no formal requirement that you do so. Most employment in the United States is called "at will", which means that your current employer can fire you at any time and for any reason (except those that are prohibited under law).