Oh no! The poor Ill Girl with cancer is being menaced by the Serial Killer! No one has survived his attacks yet, and it's going to break her fiancé's heart, and after he finally got up the courage to propose to her!
This is when the audience turns to the writer and says, "Like You Would Really Do It". Despite the author's best efforts, the audience doesn't buy the suspense or anguish that the character is being menaced with. They know the Sorting Algorithm of Mortality has this particular character dead last (pun intended) in terms of who's gonna die, and so they're just counting the seconds before the door is smashed open and The Cavalry charges in, or the bad guy goes "You're Not Worth Killing", or (if the character should actually appear dead) for the failed Fake Kill Scare to be revealed. This reaction extends not just to children or infants, but to any hero or character with thick Plot Armour in a setting where things Could Have Been Messy. Even the Heroic Sacrifice, capable of felling the mightiest of heroes, falls short of really killing them.
It's always worth remembering that in any kind of collaborative work, such as a comic book or long-running TV series, even if one author really does sincerely mean to kill off Captain Astonishoid for really reals this time, it's usually only a matter of time until another writer comes along and brings them back if the character is popular enough. As such, the notorious phenomenon of Comic Book Death is more due to this problem than to individual authors regretting their previous decisions.
Often overlaps with a Disney Death. If the story attempts to convince you that the main character is killed off even though they obviously can't be or the story would end, see Our Hero Is Dead. If this applies to lesser good characters who might otherwise be killed off, it's Immortal Hero. The Good Guys Always Win is the most common cause. Contrast Eight Deadly Words: here it is not lack of care for the characters as much as certainty that they will make it out okay.
If they actually do kill the character for real and lastingly despite audiences expectations, that's Shocking Moments. If audiences refuse to believe the character actually is dead despite the story portraying them as such, that's He's Just Hiding!.
Note that if the actor who plays the character leaves the show or worse, dies, then their character may be killed as a result, and nobody will seriously doubt that such death is final. Also, a lead character may have plot armor, but if the series is coming to its end all bets are off.