Blackmailers are reportedly sending letters to users of the Ashley Madison dating site, threatening to reveal their membership to friends and family unless they pay money.
The dating site for married people was hacked in the summer.
Security expert Graham Cluley blogged he had received "a steady stream of emails" from the site's users worried about the hack.
Mr Cluley advised anyone receiving such a letter to "ignore it".
Ashley Madison - which has the tagline 'Life is short, have an affair' - was hacked in July, and data belonging to its 33 million members was leaked on to the so-called dark web, meaning it was accessible via encrypted browsers.
A month later, police in Canada reported that two individuals associated with the leak of data had taken their own lives.
It has left many members concerned about how their data could be misused.
One such user wrote the following note to Mr Cluley: "I just received a physical postal letter to my house asking for $4,167 [£2,748] or exposed my AM account to people close to me."
In response, Mr Cluley blogged: "I understand how it would be distressing for Ashley Madison members to receive a letter like that through the post, but I'm strongly of the opinion that - in the majority of cases - blackmailers are trying their luck, hoping that a small percentage of those targeted will pay up."
He advised users to ignore the demands but also to share the letter with the authorities.
"If you pay up, there is no guarantee that the blackmailer won't ask for more," he told the BBC.
It has previously been revealed that blackmailers were sending emails to users of the dating site, asking for money.
Mr Cluley told the BBC that he received up to "half a dozen" notes a week from Ashley Madison users who had received such threatening emails but added that the news some were now also getting letters "stepped it up a gear".
He thinks it is unlikely that it is the original hackers who are sending such letters.
"Typically they like to cover their tracks," he said.
"This is more likely to be opportunists who have got their hands on the data."
He believes that hack-mailing will become a common threat in 2016.
"Increasingly we will see hackers stealing companies' databases and then demanding cash to stop them exposing the data on the dark web," Mr Cluley said.