Three days after the couple closed on the home in 2014, according to New York Magazine, Mr. Broaddus received the first of many menacing notes from someone who went only by the name “The Watcher.” The writer — whose identity the couple said they never learned — appeared to be spying on the family from somewhere nearby.

The writer noted the make of the couple’s car and the comings and goings of construction crews, and observed that the couple had three young children. He or she wrote:

Was your old house too small for the growing family? Or was it greed to bring me your children? Once I know their names I will call to them and draw them too [sic] me.

Mr. Broaddus called the police, and the couple immediately emailed the previous owners, John and Andrea Woods, asking if they had gotten such letters. They had lived in the home for 23 years without incident, Ms. Woods said — though they had received one letter from “The Watcher,” just a few days before they moved out , said Richard J. Kaplow, the lawyer who had represented the Woodses after the Broadduses sued them, on Friday.

That letter was “nonthreatening” and made “no claim of any possession” of the house, Mr. Kaplow said.

Two weeks later, another note arrived , New York Magazine reported.

“The workers have been busy,” the writer noted. “Have they found what is in the walls yet? In time they will.”

At first, the Broadduses wondered if the writer was someone who had made a failed bid to buy the house, but that theory was quickly dismissed.