Everett Johnson said his former neighbor’s face grew stern when he asked how she was doing during a chance encounter around the start of October in Fairfax County, Va. The mother from Saudi Arabia offered a surprising reply.

“I don’t know where my daughters are,” the woman told Johnson. “I haven’t seen them in a long time.”

Johnson said the woman told him that she didn’t know why Rotana Farea, 22, and Tala Farea, 16, had disappeared or where they were, and that she hadn’t communicated with them recently. The distraught mother asked Johnson what to do.

“I told her, ‘Call the police,’ ” Johnson said.

The unusual encounter came roughly a month before the sisters’ bodies were found on a bank of the Hudson River in New York City on Oct. 24 and during a period that detectives are mining for clues, police said.

The bodies, which were bound together with duct tape around the waist and ankles, washed ashore near 68th Street and Riverside Park in Manhattan. A passerby found the bodies lying on rocks beneath a pier. They were fully clothed in black leggings and fur-trimmed jackets and showed no apparent signs of trauma. A photo from the scene shows silvery duct tape tangled up with the girls legs and wrapped around their shoes.

The mystery surrounding what befell the sisters has only deepened over the past week. New York City police said they are trying to piece together a two-month gap in the sisters’ lives after they disappeared in late August, and a medical examiner is still determining the cause and manner of their deaths. CBS News reported that the examiner’s office, which has declined to answer questions, has determined that the sisters were alive when they entered the water.

Police have not revealed whether they know how the sisters got to New York City, whether they believe their deaths were homicides or suicide, or why they went missing in the first place. For young women in the social media age, the sisters had little obvious online presence. No photos of the sisters could be found before police released images from the family on Wednesday.

But Chief of Detectives Dermot Shea of the New York Police Department said investigators have begun “unraveling” some questions about the deaths after interviewing family members and other people in Virginia this week.

“There has been what I will call significant progress trying to get the complete picture of what ultimately led to the two young ladies’ being discovered,” Shea said.

For now, the situation remains murky, and some public accounts are contradictory. The sisters were reported missing Sept. 12 but were last heard from Aug. 24, Fairfax County police said. Still unclear is why family members waited nearly three weeks to file a missing-person report, but police said neither sister was believed to be in danger at that time.

The sisters were previously reported missing on Dec. 1, 2017, but were found after a day, Fairfax County police said. Authorities said the sisters were referred to county services but also said privacy rules precluded the release of additional details.

A man who identified himself as a family friend at the Farea home in Virginia said the family was “not in a position to comment” and was unlikely to want to comment in the future.

A woman whose niece attended school with the sisters in Saudi Arabia said the “sisters were very close and never apart.” She said the Fareas had looked forward to going to school in the United States and had encouraged others to do the same.

The New York Post, citing unnamed police sources, reported that detectives learned that the day before the bodies were found, the mother received a call from an official at the Saudi Embassy in Washington saying the family may have to leave the United States because the sisters had applied for political asylum.

A Saudi official said that was inaccurate and that the embassy did not know whether the Farea sisters had applied for asylum.

“The mother’s immigration status was expired,” the official said. “Immigration asked her to leave, and we asked for an extension for her and that is what the conversation was about, not the alleged asylum.”

The Department of Homeland Security said that for privacy reasons it could not comment on whether the sisters had sought asylum.

Earlier this week, the Saudi Consulate in New York City issued a statement saying that it had retained an attorney to “follow the case closely” and that the embassy had offered assistance to the Farea family.

New York police on Wednesday appealed to the public for information about the sisters, who police said may have been staying in the New York City area. Shea said authorities do know some of what the sisters had been doing.

Media outlets in New York initially reported that police were investigating the case as a suicide pact, with the young women possibly leaping from the George Washington Bridge, but investigators backed off that theory because such a long fall would have produced trauma to the bodies and motorists would have been likely to see the pair on the bridge.

The Arab News, citing unnamed family members in Jiddah, Saudi Arabia, reported that the family has rejected the idea that the sisters committed suicide.

The Arab News said family members said Tala missed her sister and had run away from home to be with her in New York City, where the family members said Rotana was attending college.

The family members told the Arab News that relatives were concerned about Tala Farea’s disappearance but called off their search after discovering that the teen was with her sister. The veracity of those reports could not be confirmed.

Johnson, the former neighbor, said the younger sister lived in a Fairfax, Va., apartment with her mother and a brother, who was around 12, and possibly an older second brother. He said he thought Rotana was living elsewhere.

He said the sisters’ father lived in Saudi Arabia and may have worked for the government there. He would visit periodically.

He said that the family moved out over the summer and that he had seen no obvious problems in the household.

“They were always pleasant,” Johnson said.

Johnson said a succession of Saudi exchange students had lived in the apartment before the Fareas. George Mason University spokesman Michael Sandler said Rotana had attended the school but left in the spring.

“The news of her death is tragic,” Sandler wrote in an email. “University officials are cooperating with police and will assist in any way we can.”

Tala attended Fairfax High School for part of the 2017-2018 school year, but a spokesman for Fairfax County Public Schools said he could offer no other details because of student privacy restrictions.

“On behalf of all members of the Fairfax High School family, we extend our deepest condolences to family, friends, and all those impacted by this event,” Principal Erin B. Lenart wrote in a message to school families this week.

Fairfax County court records show the Farea family may have been in financial distress. In 2016, family members were evicted from an apartment in Falls Church’s Skyline Towers after failing to pay nearly $1,700 in rent, according to court records. After the family moved to the apartment in Fairfax, another management company initiated eviction proceedings over a failure to pay rent, but the case was ultimately dropped.

Police said the family came to the United States in 2015.