this happen all the time. if employee accepts more money to stay, the company is given time to backfill the position, and in the best case for the company, this employee can train their replacement... probably without knowing it.

if you accept such an offer to stay, the company knows it is about money, and that you are a flight risk because as soon as a better job comes along you will be gone. the funny thing is, most everyone would leave for a better job, but by going through this back and forth you will now have a target on you (company now realizes how critcal you are to the busness and will work harder to cross train)

I have seen this from both sides, and the author made the correct decision to walk in my opinion.

if some project needs finishing, negotiate a part time contractor stint, if you feel really really nice.