Disney rectified both of the above examples, of course.
One episode of Script FicCalvin & Hobbes: The Series has Calvin and Hobbes attempting to transport their snowmen to safety. Once Calvin's mom brings him a camera, the plotline is abruptly dropped and never referred to again.
In the Battle Royale fanfiction Heads is Heads, Toshinori is left behind by everyone after the 13 living students escape the island and his ultimate fate is left unclear.
The same thing happens with the weapon that only The Chosen Mare can wield. It's the MacGuffin for the first half of the story, and then completely ignored in the second half.
Inquirius and Cookie Dough (who was a core member of Star Fleet in My Little Unicorn) don`t play any role in the sequels. According to Word of God that`s because he had no idea how to use them anymore. The same goes for Abra Kadabra, who is only there to make Goldwin come alive.
In Vinyl and Octavia Machete Their Way Through the Jungle, Vinyl's motivation for going to the jungle and fighting her way through it (alongside Octavia) is so that she can find an ancient treasure which she thinks can save her dying father. After this story, her father is never mentioned again and it's unrevealed what his fate is.
Jokes do this regularly. Because Tropes Are Tools, the intention is to slap the punchline on the listener by surprise, at which point the rest of the joke (the figurative "mouse") becomes irrelevant. Take this joke for instance:
A janitor is mopping the church when the priest grabs him. The priest exclaims that he has an important meeting he has to attend and cannot miss, but was scheduled to take confessions instead. The priest shoves a list of sins into the janitor's hands and tells him just listen to the confessions, look up the penance and tell the confessor how many "Hail Mary"s to say. The janitor doesn't mind helping, and goes into the confessional while the priest grabs his golf clubs and leaves. The people come in, the janitor looks up the sin and says the penance. This goes on just fine for a bit, until a man confesses he got a blow job. The janitor checks every page of his instructions - it's not listed. Panicking, the janitor peeks outside of the confessional and sees an altar boy walking past. "How much does the priest give for a blow job???" the janitor whispers to the altar boy. The altar boy replies, "20 bucks and a candy bar."
Now a listener who does not get the joke or has No Sense of Humor may immediately ask, "Well, what happened with the guy who is still back in the confessional, waiting for his penance?", but that is not the point of the joke - it's the Twist Ending that this was a Pedophile Priest joke. Many, many jokes count on completely dropping the story in favor of the punchline to work.
Möte i Monsunen, a song from 1935 by the Swedish musician Evert Taube (known to write all manner of gibberish and getting away with it because of his status as a national hero) has an ending very reminiscent of this trope. A sailor by the name of Fritiof encounters another sailor, and tells him of when he sailed across the seas with wild animals on board. A few of the ending lines would be something like this, translated from Swedish: "But, Fritiof, the elephant, what became of it?" "When we meet again, I will give an answer to your question" and then promptly the conversation gives place to a description of how Fritiof rows back to his boat.
The Big Pun song Twinz has an opening verse about a gangland hit gone wrong that is so catchy that it pretty much makes the song. Once the listener is told that they killed the wrong man, the hit is never mentioned again. Even worse, the video for the song covers an alternate plot that does not exist in the song.
Justin Bieber, in his song Omaha Mall, goes to check out some girls. He says they look good, but you never know in Omaha Mall and suddenly girls are never mentioned again in the song.
In James Blunt's "You're Beautiful", the first verse ends with the line "...but I've got a plan." We never find out what this plan involves, or if anything happens as a result of it. He later goes on to say that he "[doesn't] know what to do".
In LMFAO's video "Party Rock" there is an African-American gentleman telling them to put in earplugs to protect them from the shuffling zombies then he leaves and we never find out what happens to him, and then our main protagonists shuffle anyways but it's never answered as to if they succumb to the shuffling zombies, if they were faking it, or any explanation.
Yes, there is. If you watch the video for "Champagne Showers", it opens with "It has been one week since Redfoo and Sky Blu have become shuffling zombies". As for the "African-American gentleman", it can be presumed he got away safely, due to knowing how to evade the zombies and wearing the protective earbuds.
Older Than Feudalism: Homer did this in The Iliad. He went to the trouble of describing the battle between Aeneas (mortal son of Aphrodite) and Achilles. The Gods saw that Aeneas was about to be killed, and, since he was such a good servant, decided that he didn't deserve to be killed, and took him away from the battle, declaring that he would be the future king of all Trojans yet to come. Homer never mentions him again, and even the other authors of the lost epics only said that he either fled Troy after a bad omen or was captured and spared by the Achaeans. Later Greek authors said that he went to Italy. It took eight hundred years for Virgil to turn this into a Brick Joke. An EpicBrick Joke, at that!
Open up a mythology book. Chances are, if you're reading the Perseus story, you'll know that Acrisius, King of Argos, simply had bad luck when it came to having children (or at least males), and learned through the Oracle of Delphi that while he wouldn't have any luck any time soon, his daughter, Danae, would have a child that would eventually kill him. After that, everyone knows that Acrisius stuck Danae in a box and put her in the ocean, where Zeus impregnates Danae in the form of a Golden Shower, thus leading to the creation of an important hero. You never hear about Acrisius again until a long time after, especially in your text. Depending on your version, he's more or less become something of a poor man, and happens to be visiting funeral games where Perseus also happens to be playing. As Acrisius sits in the stands, a stray discus launched by Perseus strikes an unsuspecting Acrisius in the head,thus fulfillingthe prophecy that his son would kill him. The presence of Acrisius itself seems to combine this trope, Brick Joke, and some sort of Chekhov's Prophecy.
In many versions of Arthurian legend, Arthur's mother has three daughters with her first husband: Morgause, Morgan le Fay, and Elaine. The first two play pivotal roles in Arthur's life, but Elaine is typically mentioned once in passing and then never heard from again.
Elihu spends a few chapters ranting at the eponymous character of the Book of Job, then disappears and isn't mentioned in the last portion, where God rebukes the rest of Job's "friends".
A common interpretation is that Elihu doesn't get rebuked by God because his points, against both Job and the other companions, were correct. If anything he's sort of an Inversion—Job's three friends are mentioned for thirty-odd chapters before Elihu suddenly speaks up out of nowhere.
If Elihu gets it, then Satan must be fuming...one of the two main protagonists who have a bet over the temptation and scarification of Job, he isn't involved any more after the first few chapters.
In the New Testament, we never hear any word of Jesus' stepfather Joseph after the "Did you not know I would be in my Father's house" incident when He was twelve. Church tradition says he passed away some time before Jesus started his ministry.
There's a pastor's story about a nice guy whose family went off to Christmas service without him. He wasn't a believer, because he doesn't get why God would become man. After his family leaves, some birds fly into his window in in the heavy snow, and he tries to herd them into his warm barn nearby. After being frustrated in his attempts, he muses that if he were a bird, he'd be able to get them to understand. Then the church bells happen to start ringing, and he sinks to his knees as the Eureka Moment washes over him. The story ends there, with no mention of what happened to the birds.
In  the first man and woman are created by Odin and his brothers Vili and Ve. These brothers are never mentioned again anywhere, despite the obvious importance of such characters. Some people have rationalised this by suggesting that they're avatars of Odin himself, who occasionally appears as a trinity to confuse people.
In some retellings after Christianity began to merge with Norse mythology, the two were Odin's last hope for sentient life in his dying breath after Ragnarok, and segues into the Adam and Eve story of the Bible.
A two-week 1995 FoxTrot storyline had Paige getting the role of Cleopatra in the school's Anthony and Cleopatra play, (with Morton playing Anthony, of course). The story ended before the play started, with Roger noticing Paige's name in the play program. After that strip, the story suddenly ended, with no actual strips of the play being performed, and the story was never mentioned again.
In a 2010 Funky Winkerbean storyline, the title character was involved in a near-head-on collision with a woman yaking on a cell phone. This catapulted Funky into a brief Time Travel (or was it) arc. When we come back to the present, Funky's in the hospital with assorted injuries. Not a word was spoken, before or since, about Cell Phone Lady.
This 1988 Garfield strip has a blind date of Jon's named Gwen, who dresses as absurdly as he does on dates and finds him cute. Garfield even says "God made two of them!" Although she would have been a good recurring character, perhaps as a Distaff Counterpart of Jon, she was never mentioned again.
An especially egregious one is from the most recent NXT. At some point it stopped being a competition (which may very well qualify as an example itself) and was more or less third brand not unlike a lesser version of WWE's version of ECW. William Regal was eventually made matchmaker (GM for all intents and purposes) which led to a number of plotlines that were hastily resolved when it was decided NXT would tape exclusively at Full Sail University in Orlando, Florida... all except one: In the last month of the show someone was going around attacking various wrestlers. Percy Watson, Alex Riley and Derrick Bateman all ended up on the receiving end of beat downs by the unknown assailant who attempted to frame (perhaps?) Percy for the latter two attacks. However after the Full Sail tapings WWE decided not to show them until they could secure a TV deal for the revamped NXT and so it's gone back to being taped before Smackdown with all the plotlines dropped... including the mysterious backstage assailant.
Another example is the Anonymous Raw GM. After a month or so period where the Raw GM position consisted of Vickie Guerrero and then Bret Hart the GM position was instead given to an anonymous person who issued directives via emails sent to a laptop read by Michael Cole. This continued for a year before Triple H became WWE COO and the Anonymous Raw GM was almost immediately dropped with no resolution or even a hint as to who the GM was actually supposed to be. (John Cena did lampshade the plot thread just after John Laurinaitis assumed power as GM, arguing that WWE should "bring back the computer.") Almost a year later, and long after anyone cared, it was eventually revealed that it was Hornswoggle, an apparent reference to when he was equally anti-climactically revealed to be Vince Macmahon's supposed long lost son.
GTV, an hidden camera segment during the Attitude Era. It was never revealed who was behind the camera.
Eddie Izzard's Dress to Kill tour featured the 'Firework joke' which he repeatedly references throughout his performance then ends the show without telling it. It's lampshaded by several people in the audience who immediately begin asking for it. He doesn't.
Billy Connolly performed a long, long routine beginning with his account of a mysterious body found in the street in one of the more exclusive and upmarket suburbs of Edinburgh. He then meanders off into the intricacies of going to the toilet on aircraft, and how the food chain works, and the sheer logistics of so many people on board aircraft who will all need to use the toilet at some point... he gets back to the mystery corpse in Corstorphine (and its effect on local house prices) about twenty-five minutes later. By which time everyone's forgotten how the story started.
It has been speculated by a commentary on the book that Benvolio's line "That is the truth or let Benvolio die" is significant, given that he lied and said Tybalt started the fight with Mercutio (when it was the other way around). It is unlikely, however, that he was actually killed, so his disappearance remains a mystery.
At least one revision done long after Shakespeare died had one of the nobles at the end of the play announce that Benvolio was also dead. They still fail to mention how.
Another common interpretation is related to Benvolio's Meaningful Name. "Benvolio" means goodwill in Latin. He's around for all of the more comedy-like parts — perhaps Benvolio is only a metaphor after all.
In Macbeth, Fleance speaks a grand total of two lines, escapes death at the hands of the murderers Macbeth sent after him and Banquo, then...disappears. He's not even mentioned at the end. More than a bit puzzling because per the witches' prophecy, he's destined to someday be the rightful king of Scotland, and, as he's now missing and with no living guardians, it's more than a little important that someone find him.
In the epilogue to Angels In America, we see Prior, Belize, Louis, and Joe's mother are all pretty chummy with each other five years after the events of the play, but Joe seems to be pretty much forgotten.
Cyrano de Bergerac: Did Viscount de Valvert survive his Sword Fight with Cyrano at Act I Scene IV or not? The last we see about him was that his friends carried him after his defeat, and after a little mention by Roxane at Act II Scene IV, we never heard of him again.
The Taming of the Shrew starts out as a play-within-a-play; a lord and his servants trick a drunken peasant named Christopher Sly into thinking that he's the lord by dressing him up and waiting on him, telling him that he's been mad for years. They all sit down to watch a play about Katerina and Petruchio...and then they don't show up again. One ending has Sly waking up, convinced that he dreamed the whole thing and eager to try the trick of "taming a shrew" out on his own wife; however, many scholars think that it was added later and that Shakespeare never wrote it.
In King Lear, Shakespeare decides to Shoo Out the Clowns and have the Fool drop out of the plot after Act 3, even though he was a constant companion of Lear up to that point. Some stage productions interpret this as the Fool dying — perhaps influenced by the line "My poor fool is hanged" in the last scene, though most critics interpret that line as referring to Cordelia.
When Iago's plan starts blowing up in his face in Othello, Iago frantically covers his tracks and implicates Bianca in the plot to kill Cassio. Bianca is arrested and dragged off, and that's the last time she's seen. It's not even stated if she'll be released after Iago is finally exposed.
Similarly, Adam, beloved Old Retainer and sidekick of Orlando in As You Like It, disappears after they arrive in Arden. Since Adam is elderly and nearly starves to death on the journey, some productions imply that he died; scholars speculate that the actor who played him may have needed to double as someone important during the second half of the show. (Whatever Shakespeare's intention was, Adam doesn't die in the source material.)
In Henry IV Part 2, all of Prince Hal's old Eastcheap companions are rounded up and sent to prison once he ascends the throne... except for Poins, who hasn't been seen or spoken of since the end of Act 2. This is particularly jarring in The Hollow Crown, where his role is expanded considerably, but he still disappears without explanation.
Watching the original play version of Peter Pan, you might wonder, "What happened to that rich cake Hook was going to kill the Lost Boys with"? There are several answers to this question:
A stage direction after Hook enters, discouraged that the boys have found a mother, suggests that he "has perhaps found the large rich damp cake untouched".
The novel expands this as one of the Noodle Incident adventures the children have in Neverland: "[The pirates] placed it in one cunning spot after another; but always Wendy snatched it from the hands of her children, so that in time it lost its succulence, and became as hard as a stone, and was used as a missile, and Hook fell over it in the dark."
In the musical, the boys find the cake at the end of the "Wendy House" scene. Wendy tells them not to eat it, and they go inside.
Cirque du Soleil's Mystere raises this question by leaving a key character (and more importantly performer), Brian Le Petit, out of the curtain call. The answer is All There in the Manual: when Moha-Samedi hauls him out of the theater, it's for good, as Brian wasn't "part of the show" to begin with.
BIONICLE, due to its nature, has plenty of examples:
The Dark Hunters guidebook mentions that Shadow Stealer is currently coming back from a mission and is ready to face his "master", the Shadowed One. It was deemed an irrelevant Narrative Filigree and never touched upon again.
The same happened to Aphibax's secret mission to track the events on the island of Voya Nui.
Order of Mata Nui agents report in the book Bionicle World that Karzahni is training his Matoran slaves in order to conquer the outer world he just learned of. The plot had been Retconned out of the story, so he went to fight without them, taking his Manas crabs instead.
The book also mentioned that Roodaka had become the ruler of her island and will probably train her people to form an army. What became of it: Nothing, as her island was destroyed by Kaiju, and her status was never touched upon.
What more, the book revealed the Mana-Ko, formerly believed to be beastial guardians of the Big Bad, were actually secret double agents for the Order (good guys), and would be called into war. The war did happen, but they were never mentioned again.
The eponymous slime of Unicorn Jelly simply disappeared after episode 581.
Before To Save Her the author claimed it was an intended symbolic plot point about childhood, magic or something or another.
In Questionable Content the character Sara just disappears and is never mentioned again. The Cast page lampshades this by saying she was eaten by an allosaurus. Author Jeph Jacques says he just dropped her for being boring.
Sluggy Freelance had a minor one where a reader actually asked, "What happened to the demonic ferret?" The answer was, "She's still there with the other demons, I just forgot to draw her."
Get Medieval's "Where Are They Now?" Epilogue is infamously missing Oneder, Iroth's bodyguard-turned-Muslim holy warrior. In the annotated reruns, Ironychan stated that she left out Oneder (and Sir Gerard) because she felt there was nothing really left to say about them.
Also; Asher's kitten. It disappeared shortly after Asher received it and was unmentioned for months, until it reappeared after the "Trip To The Moon" arc. Ironychan has never said whether or not this was planned all along or whether the constant cries of "WHERE'S THE KITTY" caused her to bring it back.
Monette's baby, in Something Positive. The full humor and drama of an unplanned pregnancy are played to maximum effect, but Monette's baby disappears from the plot with barely a ripple (subtle clues in the dialogue reveal it was either stillborn or died very shortly after birth). Millholland lampshaded the baby's absence much later in a filler strip in which the baby turned up in a Lost and Found box.
In Original Life, it is shown that Jessica has many children (enough so that Elizabeth feels uncomfortable asking her to take time babysitting her own kids).
Elizabeth's father all but vanishes as the series goes on. This is notable since he was written as being a reasonable parent to Elizabeth as opposed to her strict mother, and backed his daughter on things like having Fisk over. One has to wonder why he had no input in his wife all but forcing their daughter to marry someone she didn't care about.
In Bob and George, on average once per Mega Man game parody, Mega Man would beat one of the Robot Masters without killing them, and for the most part they never showed up again, though they spawned numerous Epileptic Trees. However, on rare occasion they showed up again, especially Shadow Man, who became a running joke due to his stealthy nature and the Epileptic Trees about his disappearance.
Shadow Man in particular said, after his initial appearance, that he'd disappear into the background until he was needed once again, which seemed a natural set up for him to return. It was years before he really did, and at every new plot development he was tagged as possibly being behind it. One fancomic lampshaded this by having him come and say the reason he hadn't shown up again was because, as a ninja he would return and strike when least expected... but the readers kept expecting him.
Emily from Mortifer. Last appeared on this page, and was promptly never seen again. This trope was barely averted however, when a fan drew a (spoileriffic) piece of Fan ArtLampshading it, which the author saw, stating that she had completely forgotten about the character and that she would try to find a way to bring her back into the story.
Sonichu in spades. The author's wild-running attention span has caused him to start and drop so many plots and characters, it isn't even funny.
Rumors of War: Who was that walking around as Couric? Where did Penelo disappear to? What about the rest of the characters on the ship in the first Story Arc? What about all those character Nenshe recruited to the Order of Orion? (Some of these turn into Brick Jokes later in the comic.)
Averted in 1/0. By the end of the strip's run, every character that has ever appeared, even those you thought were one-off throwaway characters, has been accounted for.
In Homestuck there is Minihoof, Dirk's pet miniature pony, who has not been seen since he entered the Medium, roughly six months ago in-comic. This is kind of concerning, given that Minihoof is tiny enough to be easily crushed and it's not certain Dirk has been home to feed her...
From "Swimming!", an early episode of lonelygirl15: "Whatever happened to that girl, Cassie?" Over 430 episodes later, we're still none the wiser.
The White Parade has a variation of this. Part III sees Ean sending Allys on an errand to fetch a sandwich from the Subway across the street from the hospital where he's staying... only for it to never be mentioned again once it's retrieved.
This strange youtube video takes this trope quite literally. It features an animated mouse who just walks across the screen and then is never seen again.
The Literal Music Video for Anything For Love has Meat Loaf continue to complain about his dropped necklace long after it stops being relevant to the video's plot.
In Kung Tai Ted's review for Tiger Love, Ted becomes so disturbed at the scene where the titular tiger mauls a boy that he breaks character and asks if the child actor actually got killed.
The interstitial webisodes aired prior to The Walking Dead's second-season premiere revolved around a survivor named Hannah and her attempts to protect her family from walkers. At the end of the webisodes, Hannah (running to escape the city with her kids) manages to kill a zombie that bites her, and tells her children to run away as fast as they can before she turns. We see what happens to Hannah afterwards (she's eaten by a horde of walkers, and becomes the titular "bicycle girl" that Rick Grimes discovers in the pilot episode), but what happened to her kids?
The Nostalgia Critic invokes this trope with his "but what happened to Boomer?" rants in various movie reviews, everytime a character's fate, especially if it was a dog, is not resolved in a movie, at least for a while. If it is before the end credits roll, a short "Boomer will live!" scene is shown. Boomer was a pet dog in one of the reviewed movies.
He had one of his own with the character of "That Other Guy" (Critic's brother in-universe and Doug's brother out). What did he do after Critic died/ascended in To Boldly Flee? Mourn? Find a new writing partner? We don't know yet, even after the Critic has been back from the dead a while he hasn't reappeared.
At the end of Spoony'sUltima VI review, Chuckles the Jester is given a Sinestro Corps ring from the Gate Cleaner. Since the review, Chuckles has not been seen or mentioned and it seem whatever storyline was being set up was dropped.
In "Pega Please", the central conflict of the episode is the question of how to deal with a sleeping dragon that's spewing smoke over Ponyville: should the protagonists approach the dragon diplomatically, or just kill him? The climax comes when Fluttershy berates the dragon for using a word he's not allowed to use, then in the denouement, Twilight explains that the dragon is now "dragone". Whether the dragon left peacefully or in pieces is never clarified.
In "Pinkie's Day In", Pinkie Pie suddenly acquires two babies, apparently via kidnapping. Mr. and Mrs. Cake leave to find the babies' original parents, but they're completely unsuccessful. It becomes a moot point by the end of the episode, so the babies' origin stays a mystery.
Chakona Space features Allen Fesler's Tales of the Folly series. Chapter 2 introduces Captain Foster's cockatiels. After chapter 3, they are never mentioned again.