Multiple surgeries were performed to save her life, including removing a kidney and part of her skull.
The machine was allegedly turned off just a day after her family's funeral, which saw her mum Vivian, dad Lars and sister Annabelle laid to rest.
'Jess was a very private girl and while we're thankful for public thoughts and interest, we are just trying to honor what she'd want'.
The Dec. 26, 2017, crash occurred on the New South Wales Coast near Sydney, Australia, and was allegedly caused by a "serial traffic offender" with more than 60 convictions on his record, according to Metro.
Our thoughts are with the Falkholt's family and friends at this hard time.
'She could be in a coma for weeks or even months, she still has all the swelling on her brain.
Jessica's sister, mother and father were farewelled at a moving funeral service on Wednesday.
Following Wednesday's funeral service, Vivian Falkholt's younger brother Pail Ponticello said: 'It's a day that will be hard to erase from our memory.
"Their lives ending on a highway makes absolutely no sense".
He also thanked the "saviours" who risked their lives to pull Annabelle and Jessica from the inferno.
"Whenever he'd ask to drive somewhere I'd suggest a time for an average driver and add on some additional time for the "Lars factor" because he was so careful". We always had a good laugh.
He also spoke about the love between his sister and brother-in-law: "They are together and always will be". You will always be remembered and in our hearts forever.
Damage on the left side of the brain can potentially impact on a person's personality or memory.
Her parents and younger sister - whom Falkholt was in the auto with - each died as a result of the accident, as did the other car's driver, Craig Whitall.
Whitall was driving home from a methadone clinic when his Toyota SUV allegedly crossed into the path of the vehicle carrying the Falkholts.
An autopsy may fail to determine if any drugs were in Mr Whitall's system due to his severe injuries and subsequent fire.