Initially, Mr. Khan said in an interview, he figured the furor against his family would subside and the news cycle would move on. But nearly four years later, he said, he still receives threatening letters, emails and phone calls. (The threats are a tiny fraction of the thousands of supportive messages the family has received, Mr. Khan added.)

“We have realized that this is a very calculated scheme, a very deliberate way of causing pain in others: ‘I will utter this, then I will go quiet and then I will let my followers take it from there,’” Mr. Khan said of Mr. Trump. “This is in his operating manual — this is not unintentional or in the heat of the moment.”

After a while, the family developed a system to open unaddressed envelopes with gloves after letting the letters sit for a few days. They have a longstanding relationship with local law enforcement, who routinely patrol near their home in Charlottesville, Va. For years, Mr. Khan, a lawyer, had an automated response on his email to remind the sender that a threat sent over email is a federal crime.