Wring Every Last Drop Out of Him

You know how some character has been sick for ages and ages and ages, and how his death will be dragged out for days/weeks/months/years, until by the time it finally happens, people are no longer shocked, or no longer even care?

Yeah. This is Kill Him Already on a slow, unheroic scale, Ill Girl taken to the ultimate conclusion. It's Almost-Dead Guy for a longer duration, with less usefulness. Generally manifests in some kind of Soap Opera Disease. Probably has something to do with Death Is Dramatic, or Creator Breakdown or Downer Ending.

As a Death Trope, Spoilers ahead may be unmarked. Beware.

Examples of Wring Every Last Drop Out of Him include:

Comic Books

Aunt May.

Fan Works

A scene from Mark Latus' "Thy Kingdom Come" story, from the Sailor Moon Expanded community, has this. In the story, a portal is opened between the normal SM universe and a much Darker and Edgier Bad Future where The Bad Guys Win. The changes hinge on Calcite, who in the normal 'verse is an Aloof Big Brother who is a human-formed youma who tries to protect his family and friends from discovery, as they suffer from a genetic defect which makes them Renegades, and therefore not Exclusively Evil and thus open to destruction. But in the alternate dimension, Calcite takes this one step further, using his and his friends' abilities in a marvelous plan to imprison Metallia within himself. But to keep her contained, he has to calm her with negative emotional resonance, which leads him to commit greater and greater atrocities. And Now You Know.
- His true Moral Event Horizon comes when he reveals what he's done to the sailor senshi of his universe. Most were killed normally as they traveled to the north pole to confront Queen Beryl. But after Calcite subsumed Metallia, he then killed Endymion and Usagi, followed immediately by Beryl. The Outer Senshi tried to counterattack soon after, but were no match for him. Only Pluto escaped, having the ability to cast her soul into the future, rather than waiting to be reincarnated. Normally, the senshi's souls are born again and reincarnated in infants. Using a device invented by his Mad Scientist cousin, he tracks down the pregnant mothers of the reincarnated fetuses and brings them to his fortress, giving them the best medical care possible until the girls were born. Once that was done, he placed the infants into stasis chambers, which would allow aging only over the course of many decades. The plan was that when they reached adolescence, they would be released and, as teenagers with the minds of infants, be "mercifully" killed off. Only to have the whole cycle repeat itself.

Film

Trinity's death scene in The Matrix Revolutions managed the amazing feat of making the audience ready to scream 'JUST SHUT UP AND DIE ALREADY!' in less than six minutes. Even if it felt like six hours.
Played for laughs with the death of Amilyn in the film version of Buffy the Vampire Slayer. Staked with a ruler during of the film's climax, he doesn't die immediately, but continues flailing and and moaning all the way through the credits.

Live-Action TV

Dr. Auschlander from St. Elsewhere was diagnosed with terminal cancer in the pilot episode, and residents bet on when he was going to croak. He survived 6 seasons of crises, chemotherapy, accidents, the deaths of several major characters, before dying in the final episode. (or did he...?)
Mark Greene's death on ER.
...Which was preceded in pathos by Bobby Simone's death on NYPD Blue.
Laura Roslin on Battlestar Galactica. Twice. Notable in that although her illness only becomes majorly visible on those two occasions her very first scene had her being informed she had cancer and she spent the entire run of the show dying in varying degrees. Though on that show it is likely everybody felt they were going through this trope.

Literature

Hoster Tully from A Song of Ice and Fire lasted more than two books before succumbing - and he spent all of his appearances delirious from painkillers. In a possible acknowledgment of this, by the time he died his daughter had become inured enough to death that she barely reacted either.
Dido in Virgil's Aeneid, making this one Older Than Feudalism.
Stones from the River does it with both the main character's father and her dog, in an apparent attempt at Death by Newbery Medal.

Newspaper Comics

For Better or For Worse has made Grandpa Jim progressively sicker and sicker with strokes and heart attacks, and done several "fakeouts" of his death. And has him have yet another heart attack at the end of the strip, on the day of Liz's wedding. Yet he never actually dies until the age of 89- somehow surviving two more years (he was born in 1921) after the end of the strip!
Funky Winkerbean has Lisa who spent months slowly dying of a cancer that had returned. Every so often, there's a Hope Spot where it looks like she'll recover, but eventually she died and the creator initated a Time Skip to the future.

Video Games

Solid Snake in Metal Gear Solid 4 might qualify for this; he starts off already rapidly aging and coughing, proceeds to get the shit kicked out of him at the end of every mission, gets fried, shot, blown up, beaten, injected repeatedly for self-medication, and doesn't quit smoking. It's admirable how much punishment he can take, but Hideo Kojima is definitely punishing Snake in as many ways as humanly possible.
- He doesn't die. In fact, he actually gets better!

Web Comics

Parodied in Bruno the Bandit with 'Uncle Lucius'. He's been 'dying' in one of the Bunkleyutz's back rooms for over thirty years! No one can bear to kick him out, even though he's not actually related to them - "I thought that he was your Uncle Lucius!"

Real Life

Hospitals occasionally have to deal with these sorts of people in the real world- continually sick with some unknown illness which will almost certainly kill them (or believing themselves to be so). The term used for such unfortunate figures is GOMER- Get Out of My Emergency Room.