On most nights, a well-traveled path on the Brooklyn waterfront with sprawling views of Coney Island and the Verrazzano-Narrows Bridge grows so dark that you can barely see your shoes.
There are no streetlights or surveillance cameras along the path, known as the Shore Parkway Greenway, where the 28-year-old jogger Katie Suarez was stabbed last week an hour after sunset. As of Wednesday afternoon, she remained on a ventilator, according to a person familiar with the investigation.
Ms. Suarez, of Gravesend, Brooklyn, lived and worked near the path, where her evening jogs had become routine, the police said. During the two weeks before the stabbing, she had taken at least four runs along the same route, according to her profile on Strava, a fitness tracking website.
“She never thought that something like this could happen to her, because I would always tell her, ‘Honey, you have to be careful, you have to be careful,’” her mother, Yasira Suarez, told reporters outside her home on Tuesday. “She would say, ‘Ma, nothing is going to happen to me.’”
The Start of the Run
On Friday at 6:35 p.m., roughly half an hour after sunset, Ms. Suarez left her job at TD Bank in Caesar’s Bay Shopping Center, a waterfront retail complex, the police said.
She met her mother 15 minutes later at a Wendy’s, a quick walk from the bank. Ms. Suarez changed into her running gear, handed her work clothes to her mother and, sometime after, began to run west along the Shore Parkway Greenway.
Later, Ms. Suarez’s father, Nery Suarez, joined his wife at Wendy’s and planned to drive her and Ms. Suarez to their home in Gravesend, the police said.
The couple sat and waited for their daughter’s return.
The Attack
An hour had passed since Ms. Suarez had set out on her jog, and her parents wondered whether she was close by. At 7:56 p.m., her father called to see how much longer she would be.
“I’m about a half-mile away,” said Ms. Suarez, according to the police. It was a distance that Ms. Suarez, an avid jogger, could run in roughly five minutes.
“I should be there pretty soon,” she said.
Those minutes came and went, but there was still no sign of Ms. Suarez. Worried, her parents set out to find her. They walked west along the Shore Parkway Greenway, her father several paces ahead.
At 8:16 p.m., Mr. Suarez discovered his daughter unconscious, lying under a tree just to the side of the path, near Bay 17th Street, the police said. She had been stabbed in the neck, an injury that extended to her oral cavity.
Mr. Suarez began to scream.
A man who was walking with his girlfriend called 911, as did Mr. Suarez, the police said, and Ms. Suarez was taken to NYU Langone Hospital-Brooklyn.
A Search for Leads
On Friday night, police scuba divers searched the murky waters of Gravesend Bay as police drones whirred overhead for signs of the assailant. On the path, detectives used flashlights to illuminate the area. Other officers plodded through the tall grass, looking for any trace of evidence.
It was unclear on Wednesday what time Ms. Suarez left the Wendy’s to begin her run. It was also unclear how far, and for how long, she ran west along the greenway before turning back east to meet her parents at the restaurant.
The attack on Ms. Suarez took place next to an isolated part of the path, near a fenced-in construction site for a pedestrian bridge. The fence, covered by a tattered green tarp, appeared to block the view from vehicles on the Belt Parkway.
Electricity needed to power the cameras and lights does not extend to the path near the Belt Parkway, a thoroughfare that wraps around the southern edges of Brooklyn and Queens. Investigators who often rely on surveillance footage to solve crimes have struggled to find clues about the assailant. So far, no arrests have been made.
Still, police officials hoped that drivers saw something that might help the investigation. In a 20-minute span, about 1,700 cars passed by the spot where Ms. Suarez was attacked.
“We are looking for Teslas, we’re looking for Uber drivers — anybody that had a dash cam, just for the possibility that this perpetrator may have ran across the Belt Parkway to escape,” said Joseph Kenny, the chief of detectives for the Police Department.
Residents in the area have long known about the risks of running on the greenway after dark. “The only reason this happened — there’s no lights on the path,” said Mike Sarutto, 75, of Bensonhurst. “And there’s no police presence.”
On Tuesday evening, four days after Ms. Suarez was stabbed, the Shore Parkway Greenway remained mostly desolate, save for a police van and three officers searching the area close to the construction site. Nearby, a small bouquet of yellow flowers was tied to a railing by the water next to a single fabric rose.
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