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.

Ethics and moral is dependent on a person's principles. It's not imposed by law. If I was given any counter-offer also, I will consider, I mean if its like 50% or 60% more why not? lol...

Not really, this is normally imposed by CEO on HODs. Typically, subordinate don't know what is your immediate superior's KPI.

Some may have or some don't have but depends whether your superior share with you or not.

More pay, promotion etc... OF COZ i will come back a change person haha...

The again, those who typically get counter-offer especially before Bonus, normally get lesser or they don't get anything because they already receive earlier in their counter-offer. This is the downside, you can't eat your cake and have it too!

Yes and no. If the person is a suck up then maybe but generally people don't mind but in fact it will motivate others to jump cause they know that the company can pay more.