The notion of a work being "made available" only applies to anonymous works; for known authors, the protection is the same as for published works: life plus 50 years, which the US and some others have extended to life plus 70 years.
For written works of art, copyright generally extends to 50 years after the author dies. In Shelley's case, his work is no longer copyright protected.
It becomes part of his/her estate and passes through probate the same way as any tangible asset.
If you are not the composer of the song then you can NEVER take the copyright as yours; you would have to purchase it from the copyright owners. Also, when the copyright expires, 50 or more years after the author's death (or after publication, depending upon circumstances and national laws) it is no longer copyrighted at all and nobody can possibly own the copyright.
Generally speaking copyright in music and lyrics lasts for the life of the copyright owner (composer or songwriter), plus 50 years after the end of the calendar year in which the composer or songwriter dies. It may vary from country to country.
It would pass to their heirs unless other agreements were made.
There is no movie of yet for Love Never Dies.
Unless other arrangements were made, the rights would pass to their next of kin.
Virginia Hamilton wrote The House of Dies Drear.
Kay Thompson is the author of Eloise book dies
It Is IRA Songs
Tonight The World Dies
Under current US copyright law protection extends to the end of the calendar year, 70 years past the death of the author. The exceptions are for works published before 1964 which were properly renewed. They are protected for 95 years post publication.