J.A. Crook's Law and Life of Ancient Rome says that one of the generalizations concerning Roman commercial law is that "[t]here was no law of patent or copyright, [and] no protection for property in ideas." Rome didn't have modern technologies to speed book copying along, so most copies were made by booksellers using literate slaves as scribes. You wouldn't save much money or time over a bookseller by making a copy yourself.

Even though copyright didn't exist, plagiarism as a concept did. Vitruvius related an occasion where King Ptolemy Philadelphus of Egypt held a poetry contest, and had Aristophanes judge. Aristophanes surprised everyone by saying that the poet who least impressed the audience should win, because he is the only one who made his own poem, while the rest had stolen their poems from older works. He then proved it by having books from the library brought in order to show the source of the verses.

As for unlicensed sequels, the closest thing I can think of is the Aeneid. It's basically Illiad fan fiction written for political reasons. It takes the character of Aeneas from Troy, and has him escape the destruction of the city and go on to help found Rome.