Almost happens to Liechtenstein in Hetalia: Axis Powers, after World War I destroys her lands and kills a good part of her people.
Rin had to lie to her by putting the blame on himself so she'd recover the will to live.
Kaede Fuyou from SHUFFLE! was close to this as a young girl, after her mother's death in an accident.
Schezar's depression became worse when she learned that Leon was Dead All Along. Allen is deeply angry at his father for that.
This is what killed Allen Schezar's mother in The Vision of Escaflowne after she lost both her husband Leon (disappeared without a trace) and daughter Selena (kidnapped).
The Anti-Spiral tries to make the whole of humanity suffer this in Tengen Toppa Gurren Lagann.
Subverted/Averted as all hell in Sayonara, Zetsubou-Sensei, much to the (non) consternation of Itoshiki, a man so steeped in despair that he will Wangst himself to suicide over the most outlandish theories and observations.
then we cut to the doctor sweatdropping and saying that she only has a cold. After she hears about her idol Nagi's death, we see her in her apparent death bed, telling her daughter that, just once, she wanted to see Nagi in person.
Parodied in Negima! Magister Negi Magi with Emily Sevensheep's mother.
When his daughter, his new reason to live after Nagisa's death, dies in his arms, he collapses in the snow, presumably dead from a broken heart.
Tomoya Okazaki of CLANNAD ~After Story~.
Luckily, when Kami and Popo use Earth's Dragon Balls to resurrect everyone Frieza's forces murdered, this brings back the Elder for the amount of time his life was shortened by. It nonetheless becomes a critical plot point because Planet Namek's Dragon Balls disappear when he dies. To be fair, he was extremely old and had been dying slowly for quite a while, so it amounted to dying a matter of minutes before he would have died 'naturally'. causes this to happen to the Grand Elder of Planet Namek.
In Dragon Ball Z the stress of his people being slaughtered by Frieza and co.
She only recovered the will to live when she realized that Roy had survived. then slumped to the ground, weeping and waiting to be killed. When Lust made the Badass Boast that she had killed Roy Mustang, Riza went on a brief Roaring Rampage of Revenge until she ran out of bullets.
It could also be said that this is what almost happened to Riza.
Yes, it's true, she got sick, but it was stated that she was just never the same after Hohenheim left and that the lack of self-care between being a single mother and her broken heart weakened her enough to die from an illness she probably should have recovered from.
Also, it's implied that this is what happened to Ed and Al's mother Trisha.
This makes more sense when it's later revealed that this chimera was his wife.
Shou Tucker's first chimera dies this way by ceasing to eat and eventually dying of starvation.