Pope Benedict XVI may have resigned as of February 28,2013 but he would be able to publish works with the permission of Pope Francis and providing the works in question would not be a conflict of interest with the pontificate of Pope Francis and his successors. Will he publish anything? Probably not. One thing is absolute: Pope Emeritus Benedict XVI can never publish any official documents whatsoever. Pope Francis acknowledged the efforts of his predecessor when he published his first encyclical Lumen Fidei of July 5, 2013.
Pope Emeritus Benedict XVI is not going into solitude to hide as some believe, but is retiring from the world, in order to lead a life of prayer and contemplation.
The writings of a deceased pontiff (retired pontiff) are not to be destroyed unless explicitly mentioned in the last will and testament of the defunct pontiff. You can read about this in chapter V (part I) of Universi Dominici Gregis of Pope John Paul II. http://w2.vatican.va/content/john-paul-ii/en/apost_constitutions/documents/hf_jp-ii_apc_22021996_universi-dominici-gregis.html
Personal writings and documents of a deceased pope are to be stored in the Vatican Secret Archives and are not to be open until 75 years after the death of that pope. You can see where the works of Pope John Paul II are stored in his video. https://www.youtube.com/watch?v=urLxLj_UU8w