Extremely Overdue Library Book

A character goes to the library and checks out a book. However, they are very bad at keeping track of things, and they lose the book. Months, sometimes years later, they find the book again. The character most likely has to pay hundreds, if not thousands, of dollars in fines. Or rather, he's afraid that he'd have to.

Often a comedic Trope, it's similar to a Mattress Tag Gag in terms of severity, and can often be due to a Scary Librarian in charge of the library. Will often lead to An Aesop (as in, "don't be afraid of frivolous things") or in more whimsical settings, show how petty the bureaucracy can be.

This happens a lot in Real Life. Occasionally the story of a book due 50+ years will be added as a filler in news segments. More often than not, the library will waive the fee as the book is now decades old and can be quite historical. More recently, library fines are capped at a fixed fine (either enough to buy a replacement copy or a set time period after which the fine will stop increasing) so the fine will not break the bank of the poor old man who finds it later in life. Because of this, this trope might be a Dead Horse Trope in the future.

Examples of Extremely Overdue Library Book include:

Fan Works

Triptych Continuum: Some of Twilight's library patrons had overdue books for months, if not years.

Literature

In Diary of a Wimpy Kid: Dog Days, Greg found a book, titled How to Make Sock Puppets, which he had in his procession for a long time. He got worried that he'll get arrested if ever he returned to the library.
In Shel Silverstein's book A Light in the Attic, there was a poem about someone, who finds a book that was 42 years overdue, admits that it was theirs, and does not know what to do.

Live-Action TV

In the Seinfeld episode, "The Library", this is pretty such the entire plot as Jerry is confronted by a library investigations officer named Joe Bookman.
The Brady Bunch: In "The Private Ear" episode, one of Greg's Dark Secrets that he doesn't want anyone to know about, but trusts Marcia to never reveal ... until Peter lets on to his big brother that he knows that the librarian isn't going to be very happy and that he'd better pay up big time, and that he might have to really face the music with the folks.
This was the plot of an episode of Too Close for Comfort, where Henry found a bag full of overdue books while cleaning out the storage closet, and spent the whole episode trying to get rid of them out of fear of paying thousands in fines. Eventually, he returned them and only had to do a small amount of community service, but the true irony came after doing so, when he realized he had never actually read them and decided to withdraw them again!
In The Zack Files, the pilot episode had Zack borrowed Alice in Wonderland and it was months overdue. He tries to get it back into the library without getting in trouble, only to realize a page of it had been torn out and stolen by Vernon. Being a Weirdness Magnet, the torn page allowed the characters to come to life and put Zack on trial for the overdue book, were Vernon was eventually revealed to be the legitimate culprit.
Averted on Newhart. Larry, Darryl, and Darryl decide to make a time capsule and ask the other characters for donations. They have to dig it up after a week because one of the Darryls put a library book in it.
A different variation occurred on Step by Step. The parents become concerned with the kids renting many videotapes, some of which they never watched, in a single weekend. They're also forced to buy one movie because Brendan lost it for longer than the maximum fine. While the other kids are punished for their outrageous spending, they lay the blame on Brendan for losing the movie.
Red Dwarf: Lister's response when informed he was in stasis for three million years. "Three million years?! I've still got that library book!"

Newspaper Comics

FoxTrot: In one strip, Paige finds out that she had months-overdue library books because when she entrusted Jason to return them, he hid them in her closet.
Bloom County. In one strip Binkley was awakened by a visit from the creature that lives inside his Closet of Anxieties. The creature had found a book in the Closet and goes to fetch Mrs. McGreevy. As Binkley suddenly remembers that Mrs. McGreevy was a librarian, a giant axe was flung over Binkley's head and hits the wall. Mrs. McGreevy appeared, holding another axe, and says:

Mrs. McGreevy: 119 weeks overdue, dear...

Averted in Calvin and Hobbes:

Calvin: ...This library book was due two days ago! What will they do? Are they going to interrogate me and beat me up?! Are they going to break my knees?? Will I have to sign some confession???
Mom: They'll fine you ten cents. Now go return it.
Calvin: The way some of those librarians look at you, I naturally assumed the consequences would be more dire.

At least once in Pearls Before Swine, the librarians bring guns to enforce the returned of overdue books.

Video Games

In Kingdom of Loathing, you can find a very overdue library book in the bedroom of a Procrastination Giant. This library book was so overdue that if it weren't for the bookplate, you'd have thought it predated the invention of the library.

Web Comics

In Girl Genius Tarvek thought he must had an overdue book when he was kidnapped from Castle Wulfenbach by the Immortal Library. He was reassured his borrowing record was still perfect, but it was definitely a library not to forget to return books to.

Web Original

In The Spoony Experiment, when Spoony reviewed the 1989 fantasy film The Lords of Magick he implied that he borrowed the VHS tape from the library twenty years ago.
The owner of the game store in Acts of Gord rented out games, rather than books, but had a similar problem. A few of his customers are mentioned as keeping a game for so long that Gord simply bills the customer's credit card for the price of the game, as the late fees eventually exceed the cost of the game.

Western Animation

In one Time Squad episode, the team was visited by elderly versions of themselves from the future. They were meant to warn them about something, but due to senility, they can't remember what it was. At the end of the episode, they finally remember that they wanted to warn the present team about a library book that they should return, because the financial penalty for it being several decades overdue is astronomical.
In an Arthur episode, "Unfinished". Arthur looked for a new copy of a long-out-of-print book called "93 Million Miles in a Balloon" when the last few pages of his copy of the book are missing (and later revealed to have been in the pocket of his jacket and ruined in the wash). He finds out that the Elwood City Library did have a copy of the book, but it was checked out ten years ago and never returned, as whoever last borrowed it moved out and left no forwarding address. Ms. Turner vowed that if that man ever returns to the Elwood City Library, she will personally revoke his library card.

Real Life

Mental Floss made a list which had this trope's name all over it.
In Sept. 29, 1965, someone borrowed the book "Who Has Seen the Wind", but didn't return it until 52 years later.
Arthur Edwin Boycott checked out "The Microscope and Its Revelations" in 1894. The book wasn't returned until 120 years later, by his granddaughter.
George Washington had a book that's over two centuries overdue and that he never returned.
A priest found and returned a book that was published in 1666 to the Marsh's Library, the catch was this book was missing for 180 years.
An audiobook copy of The Adventures of Tom Sawyer was returned to the Johnson County Library after 42 years.
The "Heroes of the Middle Ages" was returned 66 years late. The Cuyahoga County Public Library calculated that the fees would've been over $2,364.
A Babar and Father Christmas book was 38 years overdue before it was returned to the L.E. Phillips Memorial Public Library.