The disappearance of Liu Huijun (劉慧君) and her 4-year-old daughter on the night of January 20, 2008:
An unknown woman and her daughter walk into the Yuanlin Finance Building (員林財經大樓) in Yuanlin, Changhua Country in Taiwan. Not recognizing them, the building's manager asks them what they're doing there. The woman replies she's there to see a friend. Then, she takes the elevator to the 11th floor.
In the CCTV footage from the elevator, the woman is seen behaving erratically and takes off her coat and shoes, as well as her daughter's coat in the elevator (in some Asian countries, there's a tradition of taking off your shoes before committing suicide). She then exits the elevator with her daughter. They're picked up by the hallway camera on the 11th floor, heading towards the stairwell. The stairwell has no security cameras, so they could've gone either up to the rooftop or down.
(I was unable to find a video with the unedited CCTV footage but
this video shows all of the footage in motion from both the elevator and the hallway.)
Then? Nothing. After the clothes are found by a security guard the next day and the manager tells him about the incident with the woman, they alert the police. The police go to the rooftop thinking they're going to find something horrible there, but a thorough search yields no results. The woman and her daughter's bodies also aren't found on the any of the balconies below the 11th floor, on the ground or on any of the rooftops of the other buildings surrounding the Yuanlin Finance Building.
At the same time, they don't appear to have left the building. Nearly all exits are monitored by CCTV cameras, but the police finds no trace of them despite reviewing hours of CCTV footage from those exits and from neighboring stores. There is an unmonitored obscure exit that the woman could potentially have used, but the door turns out to be locked and covered in dust so it clearly hasn't been used in years. The woman and her daughter simply appear to have vanished into thin air.
A breakthrough comes a few days later when the unknown woman is identified as Liu Huijun. Around the same time that her husband contacts the police, her scooter is found abandoned near the building. She was a woman who initially had plans to become a hairdresser in Taipei, but was forced to move back to her hometown of Shetou and marry a man her relatives had picked out for her. She had three children with him during the marriage.
The marriage was marred by problems as the man was a lazy alcoholic who constantly put the family in debt and beat Liu frequently. Because of this, she ended up getting a divorce from him. However, pressure from the community and her family made her marry him a second time. After the remarriage, they had a fourth child – the daughter that was seen with Liu in the elevator.
Despite swearing up and down he was a changed man before they got back together again, the husband's drinking problems actually got worse during their second marriage. It's during this time period that Liu is said to have started to deteriorate heavily. On January 19, she and her husband had an argument that would last until mid-afternoon the next day. At that point, Liu took her youngest daughter and drove off on her scooter.
Her husband initially assumed she'd just gone to her mother's house, so both he and the police were baffled when it turned out she'd gone all the way to Yuanlin that lies 8 kilometers away from Shetou. She was not known to ever have been to Yuanlin or to know anybody who lived or worked in that building. Yet, it's obvious she went to that building for a specific purpose.
It's often referred to as Taiwan's Elisa Lam case because of the similarities between the two cases.
There are a lot of theories surrounding this case. The most prevailing ones are:
a) Liu killed herself and her daughter and their bodies are still in the building but simply haven't been found. The main problem with this theory is that no foul odor (or foul-tasting water like in the Elisa Lam case) was detected by the residents of the building during the years following her disappearance. You'd think somebody would have noticed the smell of two decomposing bodies if they were still in the building.
b) Liu actually knew somebody in the building (e.g. a lover) and went to see them, but she and her daughter got murdered and then their bodies were disposed of. This theory is based on what she told the manager, and a remark she made to her eldest daughter about "going to a friend's house for a few days" on the day she had her last argument with her husband. What speaks against this theory is that nobody lived on the 11th floor and she was known to rarely socialize.
c) Liu knew someone in the building and has been hiding away with her daughter for 18 years (the police spoke to the residents after her disappearance but they weren't allowed to actually go into the apartments). This has the same problems as b) and it just seems unlikely in general that they'd be able to hide for such a long time.
d) Liu somehow found a way out of the building and went off to commit suicide somewhere else. Her going to the 11th floor was just a way to mislead the police. How did she dodge the CCTV cameras? Besides, it seems like an unnecessarily complex plan to carry out for someone who was clearly not of sound mind at the time.
e) Liu somehow found a way out of the building and ran away with her daughter. This theory has the same issues as d). Also, none of Liu's cards have been used since her disappearance and no child matching the daughter's records was found to be enrolled in any Taiwanese schools when the police looked into it in 2013 (when the daughter would've been 9 years old).
f) Liu got help from someone in the building to run away and start a new life under a new identity, maybe even in a different country. This theory has issues for the same reasons as most of the other theories, she'd have to know someone in the building and she'd have to find a way to dodge the CCTV cameras. Though it's more likely she would've left disguised if she actually did get help to leave the building.