Great authors construct distinctive "universes" for their characters to live in. Later authors sometimes continue the legacy by writing in the same universe, with the approval of the estate. Once a work has gone into the public domain the established universe is fair game to all comers.
Many authors have "picked up a dropped pen" and written further works using famous characters. Some of these works take the characters far beyond where the original author stopped.
A literary universe for a famous author includes not only new fictions but also critical analyses, biographies, adaptations for the screen, "where the characters walked", and the appearances of the characters in other works. (Or the appearance of the original author as a character -- fiction coming full circle.)
Some new fictions are done as pastiche or satire. But most come from a desire on the part of later authors to revisit a fictional universe that has become real for them because of the talent and skill of the original author.