I am currently intrigued by the number of Jane Austen sequels/prequels etc there are out there. I had a quick scout round on Amazon and came up with a grand total of 67 though I'm sure there are more than that. I then looked up www.pemberley.com - which is a largely American site devoted to all things Jane. They have a section on sequels/prequels where I found more of them - and their lists didn't include some I'd found. The site also includes fanfiction - i.e stories which fans have posted which may or may not be of any literary merit at all.
Some authors seem to have made a career out of sequels to famous novels - e.g. Emma Tennant - who has also written around the Brontes as well. I've also located one by Rachel Billington - Perfect Happiness - a continuation of Emma. I suppose one of the well known books on this sort of theme is Jean Rhys' Wide Sargasso Sea which has become a classic in its own right and deals with the early life of the first Mrs Rochester - the mad woman in the attic from Jane Eyre.
The attraction of such literary efforts must be partly that the characters are already in existence so potentially you have a ready made audience for the book. Though of course the purists may not consider them to be worth reading. Many sequels do fail to achieve the popularity of the original - the sequel to Gone with the Wind sank without trace. Many of the spin offs from Daphne Du Maurier's Rebecca have not been commercial successes.
Of course using the characters from work which is out of copyright is attractive as well, though sequels of works mentioned above have been sanctioned and even encouraged by copyright holders.
I have not checked to see whether there are any sequels to the works of Charles Dickens or Anthony Trollope. Both these authors must have abandoned minor characters who could be turned into heroes and heroines of their own stories and yet no one seems to have taken up the challenge - or not that I have heard of. Does anyone know any different?