You could certainly publish a sequel. You could also re-tell the same story in your own words using the same characters.

The elements bearing proper names in a book may be protected by trademark, but if a book is out of print and nearly impossible to find, the requirement that a trademark be continuously defended by its owner is almost certainly not being met. Plots, book titles, characterizations, settings, these elements are not protected by book copyrights. Only the sequence of words on the page is protected.

I could tell a story about a half-height man who carries a dangerous magical artifact across the continent, into the very heart of an aggressive and evil power, for the purposes of destroying it forever. I could tell a story about a plucky young heroine forced to compete in gladiatorial games by an oppressive centralized government. I could tell a story about a boy wizard who attends a boarding school for magical youth, grows in maturity and ability, then defeats a ruthless older wizard bent upon world domination.

But you can be certain that an army of lawyers would be combing through those to find out if I ever sequenced three of the wrong words together in the wrong order. If I instead ripped the story arc from a "lost" out-of-print book, there is a low probability anyone would notice, there is a lower probability that a person who noticed could locate and inform the rights-holder, and there is a miniscule probability that the rights-holder could prove infringement.

But then again, Thicke and Williams still had to pay the Gaye estate for "Blurred Lines" being too similar to "Got to Give it Up". And that raises some questions. How much of an old work can be copied before it constitutes infringement? There must be hundreds of pop songs based on Pachelbel's Canon in D. Are they necessarily derivative works, or are they written that way because that is a chord structure that humans instinctively find to be pleasing? A finite number of notes has a finite number of possible note combinations, and only a subset is aesthetically "good". If you replace two quarter notes with a triplet, is it still essentially the same song? If you transpose to a minor key, is it new? Would you have to pay a royalty every time you play the "classic blues riff"? Who would you pay it to?

This is why the public domain is important. It allows younger artists to work freely, without toiling under the heavy yoke of the old bastards that already made it and don't want to share the collective patronage of the middle-classed public with the young and hungry talents who just might try to eat their lunch.

Overly extended terms represent the political domination of old over young, and even the dead or never-alive over the living. When I can see that nothing that has been created during my lifetime will become free (speech) until long after I am dead, that makes nearly my entire culture pay-per-view, it pisses me off. It makes me want to pirate certain works that don't meet my personal standard for reasonable copyright terms, for no other reason than for political protest.

So if you find those old books, maybe do the right thing for the culture, which is not the right thing according to the law. Scan them, turn them into e-books, and seed a torrent. Then, if your grandfather or any of his friends are still alive, teach them how to download via torrent, and how to read the downloaded e-book.

It is the responsibility of the older generation to build cultural bridges with the younger. If you try to erect tollbooths and paywalls all over those bridges, no one on the other side will want to cross, and the younger generation will just create their own new, alien, bizarro culture (perhaps one where trilbys are fedoras!) without any bits of your culture in it. You will become increasingly disconnected and isolated from society as you age. Then, when you die, everything that you loved will vanish from history, just because your generation as a whole was too jealous and avaricious to give anything away.

That's the legacy of 120-year copyrights. You, in a nursing home, alone, because none of your grandkids can relate to anything you say. They don't know who Tom Mix or Gene Autry or Hopalong Cassidy are, and you don't know about Corridor Digital or Nacho Punch or UCB or College Humor. They never watched Laverne and Shirley or Happy Days or Gilligan's Island; you never played Elder Scrolls or Final Fantasy or Grand Theft Auto. You still read real newspapers; they visit aggregators, follow feeds, and read The Onion. When you stick your culture in a vault and charge admission, it immediately starts to rot, and you just might rot with it.