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Family and friends of Felix Kumi on Saturday, a day after he was fatally shot by a police officer.Credit Nicole Bengiveno/The New York Times

In a dangerous profession, it is among the most dangerous of jobs. The police officers who go undercover to arrest illegal firearms dealers can quickly find themselves at the mercy of their targets, conducting big-money transactions in close quarters with jumpy, suspicious criminals quick to draw guns.

One wrong step, and bullets will fly.

The hazards of the job were made tragically clear on Friday, when an illegal-firearms sting involving an undercover New York City officer erupted in gunfire on a suburban street in Mount Vernon, N.Y., resulting in the death of an innocent bystander named Felix Kumi.

The New York Police Department said that in the midst of the sting, a suspect pulled a gun on the undercover officer, stole the cash changing hands in the transaction and ran. When the officer opened fire, police officials and witnesses said, he shot the suspect, but he also hit Mr. Kumi, 61, who was walking to retrieve his van from a nearby repair shop.

When it comes to undercover gun buys, the only thing that is certain is unpredictability, according to police officials. Dealers must be met on their terms and turf, often in isolated, sparsely populated areas where a close-trailing backup unit can immediately be spotted, Stephen Davis, the department’s chief spokesman, said.

Ambushes and surprise assaults are constant dangers, as are unexpected encounters with law enforcement agents unaware of the sting.

“All of this exists in other police work, but you’re dealing with an instrument of death to begin with,” Mr. Davis said. “You have to be prepared to face violence.”

The operation that unfolded on Friday was typical in that little went according to plan. The suspect, Jeffrey Aristy, 28, had been under investigation for some time, and undercover officers had bought numerous firearms from him in the past, the police said. On Friday, Mr. Aristy arranged to meet an undercover officer in the Bronx. When the officer arrived, Mr. Aristy asked that they drive about a mile into Mount Vernon, a city just over the border in Westchester County, the police said.

There, according to police officials, a third man climbed into the back seat of the vehicle, put a gun to the officer’s head and demanded money. That man, a 37-year-old whom police officials have not publicly named, grabbed the buy money and fled.

The officer gave chase and — after the suspect again pointed the gun at him — started firing. The suspect, whose weapon was later found to be fake, was hit three times and was hospitalized in serious condition. Two bullets struck Mr. Kumi in the torso.

Though Mr. Aristy, the suspected gun dealer, escaped during the melee, he was later arrested, the police said. He was charged with criminal sale of firearms and criminal sale of a controlled substance.

The officer involved was a member of the Police Department’s Firearms Investigations Unit, an elite group formed in 2000. Undercover officers assigned to the unit are meticulously selected: They must play their roles flawlessly and be able to improvise and adapt in tense situations.

“It takes a little more creativity and little more scrutiny and a little more thought in selecting these people,” Mr. Davis said, “because they have to walk the walk as well as talk the talk.”

The risks must be endured, police officials say, because illegal guns are a scourge, used in many of the shootings and homicides that occur in the city. Last year, the Firearms Investigations Unit was involved in at least 15 significant gun-sale investigations in New York. One of those inquiries led to the arrest of Michael Quick, a dealer from Georgia, who authorities say sold over 150 firearms, including assault weapons, to an undercover officer. Last week, Mr. Quick was sentenced to 18 years in prison.

The unit removed about 1,100 illegal firearms from the city’s streets in 2014, mostly by making undercover purchases, the police said.

Mistakes, while rare, can be deadly.

In 2003, a series of missteps during an undercover gun buy on Staten Island led to the deaths of two detectives with the Firearms Investigations Unit, James V. Nemorin, 36, and Rodney J. Andrews, 34. The detectives were forced to allow two of the buyers to sit behind them in their car, leaving them vulnerable to a surprise attack. They were then diverted from their planned route into hilly, unfamiliar terrain. At one point, the detectives lost contact with the four units meant to provide backup.

The detectives’ bodies were later found dumped on the street.

The man convicted in the killings, Ronell Wilson, is facing a federal death sentence.

On Saturday morning, hours after being shot, Mr. Kumi died at Jacobi Medical Center in the Bronx. He was surrounded by relatives and members of his church, his daughter, Rachel Kumi, said.

“He was kind and loving and concerned and very generous,” Ms. Kumi said, wiping away tears as she sat on the stoop of the apartment building where the family lives. “If you needed anything, my father never said no.”

She added, “It’s a travesty that this happened.”

Mr. Kumi, who was born in Ghana and drove a school bus for more than a decade, had lived in Mount Vernon for over 30 years, she said. He was a devout Jehovah’s Witness and went to church five nights a week for many hours at a time.

Around a half-dozen members of Mr. Kumi’s church lingered on the stoop on Saturday morning. They sobbed, hugged and tried to comfort Ms. Kumi.

On Saturday, William J. Bratton, the police commissioner, released a statement expressing condolences to Mr. Kumi’s family.

“Mr. Kumi was blameless, and this tragedy has tested and tried his family,” Mr. Bratton said. “I pray that they may find comfort in their hope of resurrection and awakening.”