"You never know who it is," Liqin Ye recalled her niece saying.
But Zhang, a University of Illinois student, may have had a false sense of security in the United States. And that could have led to her disappearance, her family told CNN.
On June 9, surveillance video showed the 26-year-old graduate student getting into the passenger side of a black Saturn Astra.
The FBI announced this week it had found the Saturn. But Zhang still hasn't been found.
Her devastated family made the journey from China to Champaign, Illinois, in hopes of finding more answers. They don't have any. Instead, they have theories.
"It could be because she is here, and she felt that the campus is very safe, and therefore she was less guarded," Ye said Thursday.
"The other reason could be because she was to sign a lease with the landlord, and she was late, and so she was eager to be there on time," the aunt said.
"And that, perhaps, sort of triggered her to decide to get into the car. We can't think of any other reason that she would randomly jump into a stranger's car."
Ambitious student to be honored on campus
"Her mom ... being a mom, is obviously reluctant to let her go afar," Zhang's aunt said. "And her mom's thought is kind of a traditional way ... 'This is the age for you to get married, have a family. There's no need to go this far, to the United States.' "
But Zhang's father "was always a supporter in whatever her dream is."
Her dream, ever since she was a little girl, was to become a university professor.
"To be a faculty member in China, there are certain qualifications you have to meet, and as part of that you have to have broad experience in terms of your research and your study," Ye said. "And that's probably what motivated her to want to come to the United States."
Zhang also knew that the United States had the most cutting-edge research in her field, environmental sciences, her aunt said.
Despite being so far from home, "her perspective is it's generally safe in the United States," Ye said.
Zhang's father said he regularly chatted with his daughter on FaceTime.
"She assured me it was very safe," he said.
The mysterious car and driver
Authorities would not say where the Saturn was found, or who owns it.
On the surveillance video, Zhang can be seen standing by a tree as a black Saturn Astra pulls up next to her. She had a brief conversation with the driver before getting into the car.
The FBI says the vehicle appeared to be driven by a white male who circled the area before making contact with Zhang.
Zhang is 5 feet, 4 inches tall and weighs 110 pounds, the FBI said. She was last seen wearing a charcoal-colored baseball cap, a pink and white top, jeans and white tennis shoes. She carried a black backpack.
Police have asked for patience from concerned students.
"Our concern for Yingying grows with each day that passes ... while we cannot share specific details on the investigation in order to maintain its integrity and direction, we continue to make progress in our search, and we will not give up until we find her."
Police say they are searching security camera footage, local hospitals, working with ride-sharing programs such as Uber and Lyft, and checking other records.
Widespread concern in China
The number of Chinese students in the US has more than tripled since 2008 to 329,000 last year.
Zhang's disappearance has garnered widespread attention back home, with groups set up on messaging app WeChat to share information about the case.
$50,000 in rewards offered
"This is the largest award Crime Stoppers has ever granted since our inception," Champaign County Crime Stoppers President John Hecker said.
"We've been in the business, if you will, for more than 30 years. And I think that underscores the importance of how we are looking upon this particular case."
The FBI is offering an additional $10,000 reward for information leading to Zhang.
Zhang's aunt is confident her niece will be found. Every morning, she talks as if her niece can hear her.
"Every morning, when I wake up, I will talk to her and tell her to be brave," she said. "And we will find you."
CNN's Ralph Ellis, Laura Diaz-Zuniga, Carma Hassan, James Griffiths and Steve George contributed to this report.