Anne de Bourgh, daughter of the formidable Lady Catherine in Pride and Prejudice, is said to be "of a sickly constitution." It's never made very clear what this means, exactly. It may just be Anne's excuse for staying in her room and as far from her mother as possible.
Marianne Dashwood, in Sense and Sensibility, isn't normally an Ill Girl but becomes one when a nasty cold turns into a more severe illness.
Jane Austen loved playing with the trope; Anne may well be completely healthy, and her fragile health merely a suggestion her overbearing mother placed in her mind. Likewise, Marianne brought it unto herself by running out into the rain out of emotional overreaction to her lover's betrayal, something very typical for her. Unlike other ill girls, she eventually recovers and becomes a more sensible and level-headed person, or at least tries to. Jane Bennett, who briefly plays the role in Pride and Prejudice wanted to be sensible and take the carriage, but her scheming mother insisted that she ride, so that she will have to stay overnight due to the rain. The rain starts earlier than expected and Jane is soaked when she arrives at her love interest's estate, so she falls ill and has to stay there for several days.
In Ascendance of a Bookworm, Myne is a peasant girl who looks younger than her actual age due to constantly getting sick. She has no stamina, little strength and is highly prone to fevers. As such she typically needs to get other people to do physical labor for her to actually make things and, even setting that aside, is subject to a mysterious fever that could easily kill her the moment she lets her guard down.
Qwill's ex-wife Miriam is indicated to be one of these; in book 3 (The Cat Who Turned On and Off), Arch snipes at him about having sent her money and he protests, pointing out that she's in poor health. In book 23 (The Cat Who Smelled a Rat), Qwill admits to his friend Weatherby Goode that she had a nervous breakdown and was committed to an institution soon after their divorce (which her parents had talked her into doing, since they'd never approved of Qwill), and that it's been a few years since she died there.
Book #24 (The Cat Who Went Up the Creek) features Doyle Underhill's wife Wendy, who has a congenital heart condition and is under strict orders to avoid stress. Her condition eventually sends her to the hospital with a heart attack, which she fortunately survives.
Diggory's mother Mabel Ketterley-Kirke in The Chronicles of Narnia: The Magician's Nephew is bedridden and dying of an unnamed disease. She and Diggory live with Uncle Andrew and Aunt Lettie (her siblings) because they're taking care of her while Mr. Kirke has to work in India. With a little help of Aslan and a magical apple he gives to Diggory at the end of his and Polly's adventures, Mabel ultimately gets better.
Lin, Tao's wife from Daughter of Fortune. She is absolutely beautiful and even has the bound feet that Tao finds beautiful. However, she is sick with weak lungs and has a hard time moving around on her tiny feet. When she eventually dies, Tao hits the Despair Event Horizon.
Poor Lucy Westerna from Dracula, thanks to getting her blood drained by the eponymous villain. Lucy spends literally dozens of chapters slowly and agonizingly dying as Professor Abraham Van Helsing, Doctor John Stewart, her fiancé Arthur Holmwood, and American Quincy Morris do everything in their power to keep her alive using blood transfusions and putting garlic around her neck and windows, yet tragically thanks to Lucy's own ignorant and equally sickly mother removing the garlic Lucy only gets worse and ultimately dies. If that wasn't bad enough, Lucy comes back as a Vampire and Arthur is forced to stake her and Helsing and Steward chop her head off.
In Dragon Bones the trope is played with with Ciarra, who is a Cute Mute, and has blue eyes and blonde hair, but doesn't conform to Too Good for This Sinful Earth stereotypes; she's later revealed to be quite the Little Miss Snarker. She recovers from her muteness when she's away from castle Hurog for a long time. The ancient evil that tainted the place is implied to be the reason for her muteness.
Queen Ehlana, in The Elenium trilogy by David Eddings, is a variation on the trope. Under normal circumstances, she's perfectly healthy and energetic, but as it gets explained to her personal champion, she's been getting progressively more sick since her coronation, and her sickness isn't something that anyone's ever seen — her symptoms contradict each other. They eventually work out that she's been poisoned, and the poison she was given has no known cure. Except one.
Two, actually. The problem is that the first candidate had already been destroyed by a healer who knew of its healing power but not that you could use it without destroying it.
August Riefenstahl in Endo and Kobayashi Live!. He's quite old compared to this trope's norm—he died at 24 and it was the last year of his life that is plot relevant. He's always been in frail health, but the fact that his younger brother Bruno has an (Inverted case of) Big Brother Instinct on him implies he is indeed considered delicate in-universe.
In the Historical Fiction book Fabiola, the main character's servant Syra has a best friend named Caecilia, a cute beggar girl who's completely blind since birth. She's also Inspirationally Disadvantaged, as she handles herself quite well despite her poverty and disability. Since Caecilia is a Christian young woman who lives in Rome during the persecutions, she gets tortured to death.
Hazel was diagnosed with Stage IV thyroid cancer at age 13, with metastasized tumors in her lungs. This is known from the opening chapter. She plays this role to her would-be suitor, Augustus, who was once quite ill himself and thus able to understand her plight. Then, the roles are rather cruelly flipped as Augustus's cancer returns with a vengeance, making him the illboy and Hazel his (comparatively) healthy comforter during his last days. Notable in that both characters are technically ill the whole time; Hazel ultimately winds up being merely less ill than her rapidly-dying boyfriend.
Other examples include Caroline Mathers, Peter Van Houten's late daughter, and all the other girls at support group, obviously.
Michelle in Robin Cook's medical thriller Fever, suffering from leukemia and further weakened by chemotherapy.
Full Metal Panic!: Kurz Weber is stated to have joined Mithril in order to pay the hospital bills of a young girl who was critically injured in a mission he was involved in. More exactly, during the assassination of the man responsible for the deaths of Kurz's parents. Kurz, who was supposed to take the shot, stopped when he realized that the poor girl would also be hit; his Cold Sniper mentor, Wilhelm Casper, had fewer scruples and fired anyhow.
The Locked Tomb: Gideon the Ninth: The Seventh House nobility deliberately breed to keep terminal blood cancer in the family, because it lets their necromancers fuel their magic with their own dying bodies instead of siphoning ambient thanergy. However, Dulcinea's case left her too frail to use necromancy at all, and she is not expected to live past 25. In fact, she didn't, and died on the way to Canaan House, where she was impersonated by Cytherea, to whom the trope also applies.
The title character of Banana Yoshimoto's novel Goodbye Tsugumi. Tsugumi Yamamoto been ill all of her life, but still tries to live the rest at her fullest and keep interacting with those around her — specially the protagonist, her cousin Maria Shirakawa.
The Haunting Of Granite Falls has Helen, the sickly daughter or a millionaire. She is subjected to numerous treatments and forbidden from doing anything dangerous and fun, like riding. It turns out that she is not nearly as frail as her father believes, and actually quite healthy — she does have a too-short leg, the result of polio, but she can walk just fine, and doesn't need all the pills she's taking. Her father slowly realizes this when Alex, the male protagonist, comes to visit Helen and wants to play with her, doing all those activities she has been told she's too frail for.
In Edmondo D'Amici's book Heart, one of the tales about "Heroic Italian Boys" has an adult version: Marco's mother Anna in 1000 Leagues to Find Mother. She has fallen gravely sick while working abroads and is extremely depressed as well, so she refuses treatment; when Marco finally finds her, Anna changes her mind and accepts to be operated on, which saves her life. The World Masterpiece Theater series based on this story keeps this plot point as well.
Klara Sesemann is a rich girl who is confined to a wheelchair, and the titular Country Mouse Heidi is taken to her household to keep her company.
It's also implied that Heidi's Missing Mom Adelheid had epilepsy and probably died of it; i.e, Aunt Dete specifically says that she had seizures ("curious attacks, during which no one knew whether she was awake or sleeping"), which puts quite the spin in Heidi's sleepwalking later. (Thankfully, modern science has disproved the link.)
Cadpig from The Hundred and One Dalmatians by Dodie Smith, who was born nearly dead and revived, and is significantly weaker than her siblings throughout the book, requiring special provisions to be made for the journey back to London.
I Want to Eat Your Pancreas: Sakura Yamauchi, the main female character, suffers from terminal pancreatic cancer. However, instead of dying from her cancer, she is killed in a random incident after being discharged from the hospital.
Marguerite in La dame aux camélias (a.k.a. Camille) is an iconic consumptive heroine. She was inspired by the famous courtesan Marie Duplessis, a Real Life example of this trope who died at age 23, and in turn inspired the character of Violetta in La Traviata and, more loosely, Satine in Moulin Rouge!.
Older Than Radio: Fantine in Victor Hugo's Les Misérables. She subverts a few characteristics of this trope, popular in that era and genre, because her illness is named, her wizened, aged appearance is described in detail, and she dies not only of the disease itself, but from an emotional shock that her body can't bear in its weakened condition. On the other hand, she manages to soliloquize paragraphs on what she's going to do when she gets better (despite the fact that the narration says she coughs near-constantly) and win the heart of all around her. (Fantine in the musical of Les Misérables is ailing and wasting away, and also sings a plaintive song about the winter wind crying and the night encroaching, and of how she would love to see her little girl one more time before she dies. And then she dies. And her death acts as a motivator for the rest of Valjean's actions for the next, oh, ten years or so.)
The Little House on the Prairie series describes Carrie Ingalls as "pale, weak, and spindly", and she suffers from what sound like migraines. Her family (probably correctly) blames the privations of the Long Winter, when all of them would have suffered some pretty grievous malnutrition. The real-life Carrie spent her adulthood moving around the country in search of a climate that would benefit her health.
Elizabeth "Beth" March from Little Women, who at first was just a little delicate, but later contracted scarlet fever and, unlike her sisters Meg and Jo who recovered well from it as kids, the side-effects on her heart weakened her further. She later became the March family's dead little sister.
Later, there is Nay aka Feliciana, one of the family slaves and the hacienda's housekeeper. (The reader is, additionally, treated to a Whole Episode Flashback explaining her, her Star Crossed Lover and their son Juan Ángel's Dark and Troubled Past.) Feliciana ultimately dies of her illness and is heavily mourned by the whole cast.
The book María Jesús: Un milagro de amor ("María Jesús, a miracle of love") by Chilean author Ana María Figueroa is the biography of an Ill Girl named María Jesús, gathering all kinds of testimonials about how she coped with the leukemia that ultimately killed her. YMMV on how well it worked.
Julia Valerian of The Mark of the Lion spends the second book dying of an ambiguous sexually transmitted disease, too penniless to even get it properly diagnosed, let alone treated before it is too far gone. Given her promiscuous, careless, and selfish behavior in the first book, when her plight is discovered, some characters see her as someone to be pitied; others think she’s getting her just desserts.
Moshidora: Yuki Miyata's illness is not specified, aside of being a congenital one; her hospitalization requires her best friend Minami to take her place as the local Cute Sports Club Manager. Unfortunately, Yuki does NOT get better, and Minami suffers an Heroic BSoD when she dies.
The Moviegoer. Kate is taking pills to ease her general malaise.
In One of Us is Lying, Bronwyn's sister Maeve has had leukaemia at least twice prior to the novel's opening, but has been in recession for a few years. In One of Us is Next, she has a relapse scare, and keeps it to herself for weeks out of fear of what a relapse would mean.
Kate in My Sister's Keeper has leukaemia. My Sister's Keeper is a deconstruction of this type of story, showing how Kate's mother's efforts to save her daughter take a considerable toll on the whole family. Kate is actually so ill that she actually does want to die, thus she asks her sister/prospect donor Anna for help so Anna can be released from being her forced donor and Kate can die in peace.
Handle with Care: Willow has ostogenesis imperfecta, or brittle bone disease. Her mother sues her best friend and OBGYN for not telling her about a disabled child, that she presumably would have aborted.
Change Of Heart (Claire Nealon needs a heart transplant). The mother is willing to do anything for her child — but she refuses a transplant from the murderer who killed her husband.
Many of the female characters created by Edgar Allen Poe fit this type. Notable examples include the eponymous heroines of his short stories "Ligeia" and "Berenice", and his famous poem "Annabel Lee". They always die.
Gabrielle Gabrielson in The Story Of =Gabrielle by her mother Catherine. Published as a Real Life story, although there's no background info to verify it. Gabrielle, the brilliant and little daughter of a well-to-do New England couple, turns out to be Too Good for This Sinful Earth. She begins complaining of stomach pain. She informs her mother that the pain is incurable and will eventually kill her. She's right. While most of her doctors think she has hepatitis and a few dismiss her as play-acting, a tiny "shadow" on the x-ray troubles the youngest doctor enough to call for an exploratory. He finds a gigantic, malignant cancer at the base of her spine. Catherine records Gaby's last weeks, her strange speeches and experiences as the cancer invades her brain, and her quiet death. All of this takes place in a hospital, which seems unlikely until you remember this was the 1940s and people could actually afford this level of health care.
In The Sunne in Splendour has George, the Duke of Clarence, invoke this trope with his sister-in-law Anne Neville as his younger brother Richard tries to see and court her. She's not sick, and Richard and Anne eventually escape and marry. Later, however, Anne's delicate constitution catches up with her and she get an Incurable Cough of Death.
Sword Art Online: Yuuki Konno contracted AIDS when she was born. By the time she was introduced in Mother's Rosario, she was already blind, bedridden and on the verge of death in the real world.
The Two Princesses of Bamarre: Princess Meryl falls ill with the Grey Death, an incurable Mystical Plague. Much of the tragedy of the situation comes from the fact that Meryl's life ambition is to quest for the cure, while her sisterAddie has never feared the disease, believing she has the inner fortitude to overcome it. Now, their roles are reversed.
Evangeline "Eva" St.Clare is a particularly melodramatic example in Uncle Tom's Cabin. Before dying of her tuberculosis, she convinces the sympathetic characters to change their ways and resist the evils of slavery.
Mercy from The Witch of Blackbird Pond has a lame leg and poor health as a result of a fever, possibly polio, she caught as a very small child.
Wilkie Collins' The Woman in White has something of an Ill Girl Ball going between the young female characters (one suspects it's homing in on whoever it looks cutest on, given the way it goes...)
Alice in A. Sapkowski's Złote Popołudnie ("Golden Afternoon"), a retelling of "Alice in Wonderland" from Cheshire Cat's POV. In this version Alice's visit in Wonderland is in fact her DyingDream after drinking laudanum instead of her cold medication. She does get better.
Male Examples
Three male characters in Another have this. Our protagonist Kouichi Sakakibara has pneumothorax (collapsed lung),and he's hospitalized due to it for almost a month at the start of the story, making him miss his first day at his new school and thus missing several details about what will go on; Ikuo Takabayashi has a heart conditionand it takes away his life, and Daisuke Wakui is asthmatic.
"The Boy" in The Borrowers, whom Sho of Arrietty is based on, had rheumatic fever — which, up to this day, is still pretty dangerous, as it causes inflammation... of the cardiac muscles.
The main character of Donna Jo Napoli's "Breath" — subverted in that he doesn't really act the part, as he is very active throughout the story. (The epilogue to the story later explains that he has cystic fibrosis, and the story occurs during a time when nobody knew what that was, and it was a one-way ticket to an early and painful death.)
The Changeover: Jacko is being preyed upon by a sort of energy vampire, which prompts magical action on the part of his older sister.
Tiny Tim in A Christmas Carol, practically prototypical with both his weak health and his unability to walk without his crutch.
Callie's little brother Sam in Cut is a little cutie who has a severe case of asthma.
Raistlin Majere from Dragonlance. He is a sickly child to begin with, and after his health is shattered in the Tower, he suffers from a disease that resembles tuberculosis or, since it is not contagious, a very dramatic version of asthma.
Victor Frankenstein from Frankenstein: A combination of neglecting food and rest to create the Creature and the shock of seeing it alive causes Victor to develop a fever that would have killed him if not for Henry. The ensuing Trauma Conga Line of the rest of the book worsens Victor’s health to the point of frequent fevers and a two month coma, escalating in him dying from illness and despair.
Tony Makarios from The Golden Compass. His "illness" was that he had been forcibly separated from his daemon.
Jem Carstairs from The Infernal Devices has to take a drug to battle a disease he got from being tortured as a child and coughs up blood if he goes too long without it.
Smike in Nicholas Nickleby eventually dies of tuberculosis, although the disease is never explicitly named.
The plot of Papelucho en la Clínica is kickstarted when Papelucho befriends Casimiro alias "Casi", a Lonely Rich Kid who's about to be operated on. They switch places for a prank, then Papelucho is operated instead by mistake and a scared Casimiro goes home to tell his dad about it. And halfway through the book, Casimiro has a relapse in his illness and is operated for real.
Paul Strobe aka the lead male from Barbara Conklin's P.S I love you. And when he dies, he becomes the female lead Mariah's Lost Lenore.
Colin Craven of The Secret Garden, who isn't actually ill, but is weak and gets sick a lot from spending all his time shut up in his room, never leaving his bed and having hysterical tantrums. Some adaptations do make him more sick than in the original, like the anime adaptation Himitsu no Hanazono where Colin is so ill that he is at least once in the verge of death.
Toklo's brother Tobi from Seeker Bears is first shown to be seriously ill and is too weak to talk, play, and even walk. In the sixth chapter of The Quest Begins, he finally dies and is shown to be very healthy as a spirit. Toklo's Story, however, shows that he wasn't always ill. Being swept away in a river (before being rescued by Oka) was the result of the ill cub we see at the beginning of the series.
Renarin Kholin from The Stormlight Archive has a blood weakness that prevents him from fighting, which a source of angst for him, since he is part of the royal family of a warlike culture. In the second book, he says that he has epilepsy.
In Sweet Piglet, we have the Master, who dies of an unnamed terminal illness.
Truth or Dare (2000): Patrick Jordan always had trouble with his chest and was sick with bronchitis for weeks every winter. After he died under mysterious circumstances in 1959, the neighbours easily believed the official story that he had pneumonia. Josh suspects there's more to the story.
The Twilight Saga: This trope is the reason why Edward Cullen became a vampire. In 1918, a 16-year-old Edward and his mother were both dying from Spanish flu... but she used her last energies to take him to Dr. Carlisle Cullen, beg Carlisle to save her son at any cost, then die.
Linton Heathcliff of Wuthering Heights is a cowardly, emotionally manipulative Spoiled Brat Ill Boy who constantly uses his illness to get what he wants, or at least to make other people miserable.
In Jack and Jill, the titular Jack and Jill are these since they got injured in the same accident: Janet Pecq aka Jill suffers an injury to her back and almost is confined to a wheelchair, while her boyfriend Jack Minot severely breaks his leg. The book is about their shared path to recovery as well as their Coming of Age Story. Leading to Childhood Friend Romance.
In the backstory, Mrs. Minot's childhood friend Lucy Snow spent 25 years bedridden after a similar incident. She was described as pretty much a saintly figure.
Jack's Big Brother Mentor Ed is slightly delicate, but nothing too big. But all of a sudden, towards the end of the book Ed gets so sick that hedies, and poor Jack suffers a HUGE Heroic BSoD when this happens.
Sick and dying teenagers of either gender are Lurlene McDaniel's bread and butter. The cancer and disease patients are mostly female, but she's written enough dying boys to land her in this category.
Bran Stark, severely crippled after being thrown off a balcony. And then he became a Genius Cripple and Waif Prophet.
Stannis Baratheon's young daughter, Shireen, who suffered from greyscale (a disease similar to real-life leprosy) as a child. She survived, but half her face is rendered cracked and stony.
The "Sleeping Knights" guild in Sword Art Onlineis made up entirely of terminally ill players logged into the game via a special medical device calls the "Medicuboid". Yuuki (mentioned above under "Female examples") suffers from AIDS, while another member, Siune, has leukemia.
The Fall of the House of Usher: Madeline is a typical ill and dying Poe woman, similar to those in many of his other stories, but in this one her brother Roderick is also sickly and weak.
Selma Lagerlöf's Thy Soul Shall Bear Witness! has several examples:
Sister Edith is a Salvation Army worker who caught an Incurable Cough of Death while at work and has a single wish to be fulfilled: to speak with a man named David Holm, whom she has tried and failed to redeem. Little does she know that David has died of the same illness and his soul has been forcibly made into The Grim Reaper, so he can see how he has ruined other people's lives with his jerkassery. As such, David is the one who fetches Edith's soul — thus sorta fulfilling her wish.
Also David's younger brother Bernard, who also led an astray life and is dying of tuberculosis in prison, lamenting how he couldn't fulfill a promise that he made to a child. David, as the Death Cart Rider, promises to fill that vow and helps Bernard to die in peace.
In The Twelve Kingdoms, the holy beasts named kirin choose each of the rulers for the realms. If said king or queen doesn't do well and the land suffers, they get struck with a fatal illness named shitsudou, manifesting itself via Facial Markings and physical weakness that quickly kills them. Only the full redemption (which has never happened) or the Redemption Equals Death ( Joukaku of Kei and Shishou of Sai) of the sovereign can save them from death. Kirins of both genders (Hourin, Kourin and Sairin are females; Keiki is male) have gotten it due to their masters's mistakes or madnesses: Sairin and Keiki get better, Hourin and Kourin do not.
There are three ill girls and an ill boy in the What Katy Did novels:
Katy's cousin and Cool Big Sis Helen is confined to her bed, and she's described as "a cripple". She's still a sweet and kind person whom Katy adores.
In a manner similar to Jill from Jack and Jill, Katy has an accident (this time she falls from a swing) and severely damages her back, thus spending the rest of the book in treatment. She's still not fully recovered in the second book.
Amy in What Katy did Next becomes very sick while travelling around.
Phil, Katy's only brother, in the fourth book (Clover). He and his sister Clover go to Colorado so he can properly recover.
),and he's hospitalized due to it for almost a month at the start of the story, making him miss his first day at his new school and thus missing several details about what will go on; Ikuo Takabayashi has a heart condition and it takes away his life, and Daisuke Wakui is asthmatic.