Brain-dead people still have reflexes!
One of these is known as the Lazarus Sign, where a patient raises their arms in the air and folds them over their chest like an Egyptian mummy. The name comes from a bible passage where Jesus is said to have raised an man named Lazarus from the dead. The reflex is often preceded by shivering and goose bumps.
Then the patient will lift their forearms, followed by their upper arms, and then the arms fall, either touching or crossed over, towards the neck or chin. The reflex is similar to the knee jerk reflex you may have been tested on at the doctor’s office, as neither requires brainpower to occur.
Patients who are being kept alive by only life-support machines and exhibit this often confuse doctors and cause them to think that they have been reanimated. Visitors by the patient’s bedside have also been frightened or convinced that a miracle is happening.
The reflex is most common minutes after breathing apparatus has been removed from a dying patient or when doctors are testing for apnea (a suspension of independent breathing). You can watch a video of the reflex here, however if you're queasy about hospitals and people being strapped to machines, you're gonna have a bad time.