Blackmail does not necessarily end with the original quid quo pro agreed to as a result of the original extortion. The person that receives the benefit of such an extortion through blackmail is nonetheless often able to return to the well, time and time again, based only on the capacity and willingness of the victim to continue to pay.
There's a real market failure when you are trying to pay for exclusive control of information, which is these days an infinitely duplicable product.
Thus, blackmailees murdering blackmailers is a staple of old-fashioned detective shows. These kind of market failures call for government regulation. But what kind?
The legal system helps facilitate some kinds of blackmail by using the power of the state to enforce the contract on both parties, getting around this market failure problem with blackmail. For example, in 1994 Michael Jackson paid $22 million to his blackmailer in return for future silence. Since this was the settlement to a lawsuit, the agreement, including the plaintiff's future silence, was legally enforceable, which presumably increased Jackson's willingness to fork over $22 million. After the settlement, the plaintiff refused to testify in a criminal trial and the prosecution of Jackson collapsed.
On the other hand, the American legal system sent Bill Cosby's alleged natural daughter to prison for five years for attempting to barter her silence for $40 million.
It seems like there is kind of an excessively fine line here between becoming a millionaire or going to prison. I'm sure that somebody out there could persuasively explain the legal distinctions that take one person who knows a celebrity's secret to a life of luxury and another person to a prison cell, but it seems rather hazy.