In the final two months of the 2020 campaign, President Donald J. Trump, his grip on power slipping because of his handling of the pandemic, desperately tried to change the narrative by attacking the business dealings of Joseph R. Biden Jr.’s son Hunter, invoking his name publicly over 100 times.

At the same time, another effort was underway in secret to try to expose the contents of a diary kept the previous year by Mr. Biden’s daughter, Ashley Biden, as she underwent treatment for addiction.

Now, more than a year later, the Justice Department is deep into an investigation of how the diary found its way into the hands of supporters of Mr. Trump at the height of the campaign.

Federal prosecutors and F.B.I. agents are investigating whether there was a criminal conspiracy among a handful of individuals to steal and publish the diary. Those being scrutinized include current and former operatives for the conservative group Project Veritas; a donor Mr. Trump appointed to a political position in the final days of his administration; a man who once pleaded guilty in a money laundering scheme; and a financially struggling mother of two, according to people familiar with federal grand jury subpoenas and a search warrant who spoke on the condition of anonymity to discuss an ongoing investigation.

Extensive interviews with people involved in or briefed on the investigation and a review of court filings, police records and other material help flesh out elements of a tale that is testing the line between investigative journalism and political dirty tricks.

The investigation has focused new attention on how Mr. Trump or his allies sought to use the troubles of Mr. Biden’s two surviving children to undercut him.

The inquiry has also intensified the scrutiny of Project Veritas. Its founder, James O’Keefe, was pulled from his apartment in his underwear and handcuffed during a dawn raid last month by the F.B.I., two days after a pair of his former employees had their homes raided.

The group — which purchased the diary but ultimately did not publish it and denies any wrongdoing — has assailed the investigation. And it has been making a case in court and to Congress that, despite its use of undercover stings and other deceptive tactics, it is practicing a form of journalism that deserves the same legal and constitutional protections afforded news organizations.

Asked a list of specific questions related to the investigation, a lawyer for Project Veritas, Paul A. Calli, responded with a statement from Mr. O’Keefe criticizing The New York Times.

Roberta Kaplan, a lawyer for Ms. Biden, declined to comment.

The episode has its roots in the spring of 2020, as Ms. Biden’s father was closing in on the Democratic presidential nomination. Ms. Biden, who has kept a low profile throughout her father’s vice presidency and presidency, had left a job the year before working for a criminal justice group in Delaware.

She was living in Delray Beach, Fla., a small city between Miami and West Palm Beach, with a friend who had rented a two-bedroom house lined with palm trees with a large swimming pool and wraparound driveway, according to people familiar with the events. Ms. Biden, who had little public role in her father’s campaign, had earlier been in rehab in Florida in 2019, and the friend’s house provided a haven where she could avoid the media and the glare of the campaign.

But in June, with the campaign ramping up, she headed to the Philadelphia area, planning to return to the Delray home in the fall before the lease expired in November. She decided to leave some of her belongings behind, including a duffel bag and another bag, people familiar with the events said.

Weeks after Ms. Biden headed to the Northeast, the friend who had been hosting Ms. Biden in the house allowed an ex-girlfriend named Aimee Harris and her two children to move in. Ms. Harris was in a contentious custody dispute and was struggling financially, according to Palm Beach County court records. At one point in February 2020, she had faced eviction while living at a rental property in nearby Jupiter.

Shortly after moving into the Delray home, Ms. Harris — whose social media postings and conversations with friends suggested that she was a fan of Mr. Trump — learned that Ms. Biden had stayed there previously and that some of her things were still there, according to two people familiar with the matter.

September 2020: Project Veritas Obtains the Diary

Exactly what happened next remains the subject of the federal investigation. But by September, the diary had been acquired from Ms. Harris and a friend by Project Veritas, whose operations against liberal groups and traditional news organizations had helped make it a favorite of Mr. Trump.

In a court filing, Project Veritas told a federal judge that around Sept. 3, 2020, someone the group described as “a tipster” called Project Veritas and left a voice message. The caller said “a new occupant moved into a place where Ashley Biden had previously been staying and found Ms. Biden’s diary and other personal items.”

The “diary is pretty crazy,” the tipster said on the voice mail, according to a Project Veritas court filing. “I think it’s worth taking a look at.”

In a recent letter to Congress, a lawyer for Project Veritas said it had been told the items had been abandoned in a room where Ms. Biden had stayed.

Project Veritas has acknowledged buying the diary, through an unnamed proxy, from two people it identified in court filing as “A.H.” and “R.K.,” but said it was told they had acquired the diary lawfully.

People involved in the case have identified “A.H.” as Ms. Harris and “R.K.” as Robert Kurlander. Mr. Kurlander, a self-described venture capitalist, is a longtime friend and former housemate of Ms. Harris. In October 2020, days before the election, Mr. Kurlander said on Twitter: “Where are Biden’s two kids?” adding, “Ashley and Hunter are disasters. Reflection of the parents.”

In 1994, Mr. Kurlander pleaded guilty in federal court in Florida to a conspiracy count in a drug-related money laundering scheme that also led to a guilty plea from David Witter, the grandson of the founder of the investment firm Dean Witter. Mr. Kurlander was sentenced to 40 months in prison.

Ms. Harris “is fully cooperating with the investigation and will remain responsive to the government’s requests for evidence and for her version of events,” her lawyer, Guy Fronstin, said in an email. “When the facts emerge it will be clear that my client has information relative to the investigation but no culpability.”

Outside his house last month near a golf course in Jupiter, Fla., Mr. Kurlander declined to comment, but a woman with him acknowledged they had been dealing with the matter and wanted to avoid public attention. She provided the name of their lawyer, who declined to comment.

A Possible Link to Trump Supporters

Mr. Kurlander also provides a potential link to the possible role of a number of Trump supporters. Among those whose conduct is being scrutinized in the investigation is a woman with ties to Mr. Trump, Elizabeth Fago, a Florida businesswoman and Trump donor who was nominated by Mr. Trump in December 2020 to the National Cancer Advisory Board.

Ms. Fago appears to know Mr. Kurlander. A picture on social media shows them dining together in July 2020. Investigators are also looking at the role of Ms. Fago’s daughter, Stephanie Walczak.

Ms. Fago visited the Trump White House at least twice. Her son, Joey Fago — a real estate agent who this year worked with Donald Trump Jr. and Kimberley Guilfoyle on their purchase of a $9.7 million Florida mansion — posted a video of him and his mother at the White House on election night in 2020 and at a Christmas party the next month, where they can be seen in the West Wing.

She and her son also met Mr. Trump on the tarmac of the West Palm Beach airport in 2019 and another picture shows the two together. In 2016, she co-hosted a fund-raiser for Mr. Trump at his club at Mar-a-Lago.

That year Ms. Fago gave $15,400 to pro-Trump fund-raising committees and an additional $7,600 to the Republican National Committee after Mr. Trump won the party’s nomination. In October 2020, she gave $500 to pro-Trump committees.

It remains unclear how Ms. Harris and Mr. Kurlander made contact with Project Veritas and what role others might have played in facilitating the transaction.

Ms. Fago did not respond to requests for comment. Ms. Walczak declined to comment.

Spokesmen for the F.B.I. and Justice Department declined to comment.

Using the Diary as Leverage

Less than a month before Election Day, in an Oct. 12, 2020, email that Project Veritas included in a court filing, Mr. O’Keefe told his team that he had made the decision not to publish a story about the diary, adding: “We have no doubt the document is real” but that reactions to its publication would be “characterized as a cheap shot.”

But Project Veritas was still trying to use the diary as leverage. On Oct. 16, 2020, Project Veritas wrote to Mr. Biden and his campaign that it had obtained a diary Ms. Biden had “abandoned” and wanted to question Mr. Biden on camera about its contents that referred specifically to him.

“Should we not hear from you by Tuesday, October 20, 2020, we will have no choice but to act unilaterally and reserve the right to disclose that you refused our offer to provide answers to the questions raised by your daughter,” Project Veritas’ chief legal officer, Jered T. Ede, wrote.

In response, Ms. Biden’s lawyers accused Project Veritas of threatening them as part of “extortionate effort to secure an interview” with Mr. Biden in the campaign’s closing days.

Ms. Biden’s lawyers refused to acknowledge whether the diary belonged to Ms. Biden but told Mr. Ede that Project Veritas should treat it as stolen property — the lawyers suggested that “serious crimes” might have been committed — and that any suggestion that the diary was abandoned was “ludicrous.”

Ultimately, one of Ms. Biden’s lawyers, Roberta Kaplan, told Mr. Ede: “This is insane; we should send to SDNY.” Shortly thereafter Ms. Biden’s lawyers alerted prosecutors at the United States Attorney’s office for the Southern District of New York, which is now overseeing the case.

In the midst of this exchange, a conservative website, National File, published excerpts from the diary on Oct. 24, 2020, and the full diary two days later, though it got little attention. The site said it had obtained the diary from someone at another organization that was unwilling to publish it in the campaign’s final days.

Mr. O’Keefe’s lawyers said in a court filing last month that Project Veritas arranged for Ms. Biden’s items to be delivered in early November to the police in Florida, not far from the house where she had left them. As the investigation came to light last month, Mr. O’Keefe said in a statement that “Project Veritas gave the diary to law enforcement to ensure it could be returned to its rightful owner.”

But a Delray Beach Police Department report and an officer’s body camera video footage tell a somewhat different story. On the morning of Sunday, Nov. 8 — 24 hours after Mr. Biden had been declared the winner of the election — a lawyer named Adam Leo Bantner II arrived at the police station with a blue duffel bag and another bag, according to the police report and the footage. Mr. Bantner declined to reveal the identity of his client to the police.

Project Veritas has said in court filings that it was assured by the people who sold Ms. Biden’s items to the group that they were abandoned rather than stolen. But the police report said that Mr. Bantner’s client had told him that the property was “possibly stolen” and “he got it from an unknown person at a hotel.”

The video footage, which appears to be a partial account of the encounter, records Mr. Bantner describing the bags as “crap.” The officer can be heard telling Mr. Bantner that he is going to throw the bags in the garbage because the officer did not have any “information” or “proof of evidence”

“Like I said, I’m fine with it,” Mr. Bantner replied.

But the police did examine the contents of the bag and quickly determined that they belonged to Ms. Biden. The report said the police contacted both the Secret Service and the F.B.I., which later collected the items.

Patricia Mazzei William K. Rashbaum Kitty Bennett Matthew Cullen and Kirsten Noyes contributed reporting.