For most people, losing their lives is the worst thing they could possibly imagine - but in anime, there are some things that are worse than that.
Anime characters who suffer a fate worse than death are sometimes immortal, like Joseph from The Ancient Magus Bride or Hidan from Naruto. These characters must endure situations that would destroy anyone else, for eternity. Other characters like Rika Furude of Higurashi no Naku Koro Ni are forced to repeat the same terrible experiences on an endless loop. Others, like Ymir of Attack on Titan, lose their sense of self entirely. All of them suffer immeasurably, to the point where passing away would be a relief.
The fact that a character is featured on this list doesn't necessarily imply that they shouldn't be alive - and it definitely doesn't imply anything about people in the real world who might have gone through more realistic versions of some of these experiences. It just means that what these characters have endured is so horrible that most people would not be able to bear it.
Nina Tucker and her dog Alexander are perhaps the most classic examples of this trope, but that doesn't make their story any less tragic. Nina's father, Shou Tucker, is a state alchemist who needs to prove his accomplishments in order to maintain his standing. Rather than actually attempt to make something happen for real, he fuses his pre-school aged daughter's body with that of the family dog. While she's still able to communicate to some degree, her existence is perceived as so utterly miserable that Scar decides to take her life out of mercy.
Anyone who descends into the Abyss and then tries to return risks incurring its curse. The curse can cause severe illness or death, and it can even cause its victim to lose human form. Mitty, a little girl who is forced to submit to an experiment that plunges her into the Abyss' depths via an elevator and then brings her back up again, suffers the latter. Her body melts into an unrecognizable puddle, forming a monster covered in pink fur. Not only is Mitty unable to communicate, she's also nearly immortal.
At first, that immortality is a source of excruciating pain, because the experimenters who transformed her body repeatedly destroy it to try and find her limit. When Nanachi, a friend whose body has also been dramatically changed by the Abyss, decides to run away with Mitty, the ceaseless pain stops - but she's also unable to care for herself, and will have to live alone for eternity once Nanachi is gone.
To spare her this terrible fate, Nanachi gets Reg to use a fatal attack on Mitty, putting her to rest once and for all.
If you don't want to suffer a fate worse than death, don't fight Kurama. When Elder Toguro tries this, he meets with an excruciating fate. Kurama plants a parasitic tree in his body, which not only drains his life force, but also forces him to hallucinate an endless battle with Kurama in which he never manages to land a hit, and is constantly mocked for his failure. In most cases, the parasitic tree would eventually consume its victim entirely, but because Elder Toguro is functionally immortal, this state of affairs will continue for all time.
In the world of Fire Force, human beings spontaneously combust, becoming what is called Infernals. However, they don't just burn up and disappear - they become fire-spewing monsters who destroy everything around them - including the people that they love - sometimes still retaining their consciousness. The titular Fire Force is tasked with putting Infernals to rest, both for the sake of public safety and for the sake of the Infernals themselves.