After 50 years, the Ted Kennedy Chappaquiddick incident has remained one of the biggest mysteries surrounding the Kennedy family.

The car crash on the US island ended the life of 28-year-old Mary Jo Kopechne and derailed Ted Kennedy’s presidential chances.

On the evening of July 18, 1969, the then US senator Kennedy hosted a party on the small island for the Boiler Room Girls, a group of six women who had worked on his brother Robert F. Kennedy’s presidential campaign the year before. One of the women was 28-year-old Kopechne.

Despite extensive reports on the incident, details of the events of the night have remained shrouded. Kennedy reportedly left the party with Kopechne, even though she did not bring her purse or hotel room key with her. The two drove off in his 1967 Oldsmobile Delmont 88.

Kennedy said the car went over the bridge into Poucha Pond after he made a wrong turn. While he managed to escape the sinking vehicle, Kopechne remained trapped and was later found dead in the morning.

But a letter to Kopechne’s surviving family has challenged this story.

The letter, recently revealed by PEOPLE’s Cover-Up podcast, came from a man who claimed to have met a woman who had attended the party the night Kopechne died.

The woman, referred to as “Betty”, said Kopechne had had too much to drink at the event. Betty then brought Kopechne to Kennedy’s car to rest, and then went back to the cottage.

The letter claimed that Kennedy and another female guest went for a drive in the car. When the sedan plunged into the water, Kennedy and the passenger survived and returned to the party, unaware that Kopechne had been in the vehicle all along.

Betty shared the story, and the letter said that was when “…the Kennedy damage control machine kicked in and informed the shocked senator.”

After receiving the letter in 2018, Kopechne’s cousin Georgetta Potoski said the full story might not yet be revealed. 

“I’m not convinced the mystery has been solved,” she told PEOPLE. 

“I know there are things that we do not know about what happened that night. The truth, even if it’s not what you want to hear, at least has some dignity around it.

“I don’t think there will ever be justice for the loss of her life. [But] I think the truth would make our hearts rest easier.”

A week after the incident, Kennedy pleaded guilty to leaving the scene of the accident and was given a two-month suspended sentence. Later on the same day, he gave a national broadcast statement in which he said, “I regard as indefensible the fact that I did not report the accident to the police immediately.”

Kennedy, who was preparing for his presidential run, delayed his campaign until 1980. His run for the country’s top office was unsuccessful, but he continued to be re-elected as senator seven more times until his death in 2009.

In his posthumously published memoir True Compass, Kennedy described the incident as “a horrible tragedy that haunts me every day of my life”.