Raymond Facey pulled his car, a borrowed Toyota, to the side of the Cross Island Parkway. The young woman told her father that she had found inexpensive tickets to Jamaica, his native country, where he was planning a family vacation later this year and where he planned to retire.

But the conversation took a strange turn, when the daughter, Dahlia Facey, 21, heard her father talk of a man approaching his car.

"Who are you running from?" she heard her father say, according to several relatives and friends. It was the last known words of Mr. Facey, who was killed with a single bullet to his head.

It was Mr. Facey's conscientious character — a trait admired by family and friends so often on the receiving end of his kindness — that placed the Brooklyn truck driver and father of four known as Brian in the path of a killer Tuesday morning.

"He was a law-abiding citizen," said Patricia Lionel, a close family friend. "He didn't want to get a ticket or cause an accident by talking on the phone and driving, so he pulled over to the side of the road to talk to his daughter."

The police said Darrell Fuller, a parolee who had served time for attempted murder, first shot and killed a Nassau County police officer on Tuesday during a car stop near 241st Street and Jamaica Avenue, a few feet outside the Queens border. Mr. Fuller exited his Honda and fired at Officer Arthur Lopez, 29, who was not wearing a protective vest, hitting him in the chest, the police said. Then he fled in the Honda south on the Cross Island Parkway, where he came upon Mr. Facey.

"He was on the phone making plans to travel to go to Jamaica with his wife and kids," said Mr. Facey's sister, who spoke only on the condition that her name not be published in order to protect her privacy.

Mr. Fuller yanked Mr. Facey out of the driver's seat and shot him in the head, the police said; he then sped off in the Toyota, leaving Mr. Facey dead next to the abandoned Honda, they said. Mr. Fuller left the hijacked car in Queens Village and fled on foot.

After a manhunt, police officers responding to a 911 call of shots fired on 111th Avenue in St. Albans, Queens, found Mr. Fuller in a minivan with two gunshot wounds: one to the right shoulder and another to the right thigh, the police said, clarifying conflicting reports Tuesday night that he had been shot in the torso or once in the shoulder. The police said they believed Mr. Fuller had shot himself, but declined to say if his weapon had been recovered.

Mr. Fuller, 33, was arrested and taken to a hospital nearby. On Wednesday night, he was released and taken by the police to Nassau County Police Headquarters in Mineola, the police said.

On Wednesday, an armful of bouquets sat on the front step of the modest Babylon home on Long Island where Officer Lopez, an eight-year police veteran, had lived alone. There was little on the quiet, leaf-speckled street or in the yards dotted with Halloween decorations that resembled the setting of his killing.

In this placid patch of Suffolk County, Officer Lopez's brethren — a small group of plainclothes officers — emerged from his house, some carrying his uniforms and belongings.

James Carver, the president of the Nassau Patrolmen's Benevolent Association, said he wanted to know why Mr. Fuller was out on parole after serving less than four years on the 2005 attempted-murder conviction in Queens and after being arrested in 2010 on charges of possession and sale of drugs in Nassau County.

At the time of Mr. Fuller's arrest on drug charges, he was a passenger in a car driven by someone who was caught selling drugs out of the car, said John D. Byrne, a spokesman for the Nassau County district attorney.

Mr. Byrne said in a statement that there had been insufficient evidence to prove that Mr. Fuller "had advanced knowledge of the arranged transaction, or handled the drugs or the drug proceeds." Prosecutors negotiated a deal that required Mr. Fuller to plead guilty to a misdemeanor charge of criminal facilitation and accept one year in prison, Mr. Byrne said.

Mr. Facey's family lamented the randomness and heartlessness of the shootings. "It's hard; it's so hard," said one of Mr. Facey's cousins, who stood in the doorway of her home in South Ozone Park, Queens, on Wednesday. "One in how many million? And it happened to him; such a good person."

At the backdoor of Mr. Facey's home on Fountain Avenue in East New York, Brooklyn, a next-door neighbor, Tamika Belches, 36, said: "In the summer he would come out here and mow his grass. And when he was done, he'd keep going and mow everybody else's, too."

Ms. Lionel, the close family friend, said Mr. Facey loved playing dominoes and listening to reggae music. He liked "to boogie," she said, laughing. When Ms. Lionel's daughter got married, Mr. Facey paid for the $1,000 wedding cake, she said. "She couldn't believe her eyes when she saw that cake," Ms. Lionel said. "She couldn't believe that he would give her a gift like that."

Christopher Maag contributed reporting.