Rewriting a copyrighted text is only permissible to the extent that the new text restates material from the original text without copying any artistic expression. It's also permissible if the new writing is considered fair use or qualifies for another allowable exception. If the original text is merely rewritten with minor stylistic changes and creative elements are used from the original text, the author of the new text could potentially face a lawsuit for copyright infringement for usurping the rights of the original author.
Rights
Copyright holders maintain the rights to reproduce their copyrighted work, to distribute copies of the work, to perform the work publicly, to display the work and to make a derivative work based on the original work. If a third party infringes any of these rights, the copyright holder can sue for copyright infringement.
Derivitive Works
A derivative work is a work based on an existing work. Because the right to make derivative works is reserved solely by the original copyright holder, any attempt to rewrite a copyrighted text must not fall within the purview of a derivative work. Therefore, a rewritten text of a copyrighted work cannot contain any portion of the original work other than facts or other aspects of the original work that are not protected under copyright law.
Fair Use
Copyrighted works may be rewritten if they are in the public domain or if the use of the original work would be considered fair use under copyright law. Fair use is not a right to use a copyrighted work but rather a defense to charges of copyright infringement. Classic examples of fair use include using another work for the purpose of critical comment or parody or using the work in a purely academic setting.
Protectable Elements
Even if you are rewriting the majority of an original text to avoid violating copyright law, several individual elements of a text may be protected by copyright law. These include the setting, characters and plot of a story. Therefore, authors need to be extremely careful when attempting to rewrite copyrighted texts.