A "last-ditch appeal" by the Italian ambassador and the Pope, to grant Alfie citizenship of Italy to take him for treatment at a hospital in Rome, failed on Monday. But Alder Hey doctors and independent medical experts say there is no cure and no hope for Alfie.
The medic said the hospital feared that in the "worst case" Alfie's family would try to take the boy overseas.
Earlier in the week, the trust made the following statement after the protests caused "significant disruption" to its service; "the hospital experienced significant disruption, due to a large protest concerning one of our patients".
The youngster's parents have mounted a challenge to the High Court in Manchester, arguing that he should be allowed to continue treatment and fly him to a hospital in Rome.
Alfie Evans cuddles his mother Kate James (left) at Alder Hey Hospital, Liverpool, England.
His life support machine was switched off on Monday, but his dad Thomas Evans said he survived through the night and is still breathing.
The judge Mr Justice Hayden ruled in Februarys doctors should stop providing life support against Alfie's parents' wishes. "It seems inconceivable that there is no way to make that happen".
Alfie is a 23-month-old toddler who is in what physicians have described as a "semi-vegetative state" due to a mysterious degenerative neurological condition that doctors at Alder Hey Hospital have not been able to properly diagnose.
Alder Hey Hospital said it wouldn't be offering a running commentary on Alfie's condition.
The European Court of Human Rights on Monday rejected a case from British parents who want to take their terminally ill toddler to Italy for treatment instead of allowing a United Kingdom hospital to remove him from life support.
He has previously been granted Italian citizenship by the Ministry of Foreign Affairs of Italy. They said that they wouldn't discuss confidential details about Alfie's medical condition, but that British doctors' guidelines call for ending treatment if the treatment is either unlikely to extend the child's life "much longer", or might prolong life "but will cause the child unacceptable pain and suffering".
The head of the Bambino Gesu Pediatric Hospital, Mariella Enoc, traveled to Liverpool to make an in-person bid to have the boy transferred to the Vatican facility. She can actually go to sleep next to him.
The judge said, in fact, the hospital had provided "world-class" care for the child. "The point is that the parents should be free", Williams said. In December of that year, the sick toddler suffered a chest infection and was hospitalized for seizures.
"If there were a more constructive attitude from the family might other options become possible, away from Alder Hey?"
The case drew worldwide media attention with the Vatican becoming involved and even US President Donald Trump tweeting his support.
Francis has spoken repeatedly about Alfie.
But a doctor treating Alfie, who can not be named for legal reasons and appeared in court in medical scrubs, said that would require a "sea change" in the attitude of Alfie's family.
Three days later, Francis again brought up Alfie, this time in his Wednesday general audience.
Just before Alfie was removed from the ventilator, the Italian Embassy in London warned, "If you remove the ventilator from Alfie Evans, we will file a complaint against you for the murder of an Italian citizen".
The boy's parents were not in court Tuesday; Williams said they wanted to be at the hospital, at their son's side.
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