He should not accept the counter offer. Its ethically wrong.

Let's say the head counter offered, when the resigned staff has already signed a letter of offer.

So your question, if the resigned staff forgo the signed letter of offer and take the counter offer, would there be any repercussions?

Well, yes and no, depends how petty the new employer is. A letter of offer, when signed becomes a contract. The key ingredients of a contract is an offer, acceptance by the other party, consideration (i.e. salary) and intention to enter into the contract. When it comes to suing the person concerned by the company, it's not so straightforward because the company must show that it has suffered some form of loss as a result of the employee not honoring the terms of the letter of offer. Considering the legal fee, time spent and possibility of recover via enforcement action, its very likely to be a futile exercise.

So the not so petty company, will typically blacklist you in their record or snitch on what you did with other recruiters/ industry players.

As to whether counter-offer is a ethical or not? That really depends how you extracted the concession in the first place. If the company genuinely decides to retain you (in your scenario) then it's alright because everything is negotiable. There are also companies who force you to sign their letter of offer to get your commitment on the spot. So the HR business is kinda dirty at times.

That being said, the most unethical behavior that I know of is that the person has no intention to join the other company, and she takes the offer letter and show it to her current employer to extract a counter offer.

It's actually a KPI for head of departments. High turnover reflect poorly on your leadership to lead a team.

It also time consuming/costly for HR to keep recruiting and looking for candidates. From what I gather the weightage is not that significant (example 5%) also but easy to get like going for training/self-improvement.

So its ur chance to throw letter and expect to get counter offer.

But why head kpi affected due to staff turnover? Ppl come and go is normal

There is always risk when accepting new offer bah, countered jor can stay with higher pay and doing the same shits, OK bah if u have been working in the com for long time and in comfort zone jor. Personal choice bah
Knowing a friend gatal gatal go join another com but later kena retrench pasal kena cut cost. Worked few mths jek now cry mama papa nka