The term completist, as applied to book collectors, has always struck this writer as something of a misnomer. In one sense, the term certainly is applicable: i.e., it describes the attempt to collect everything a particular author ever wrote, or everything a particular publisher ever published, or everything ever written about a particular topic. On the other hand....
One can only collect what is published (or otherwise becomes available) during one's lifetime. If a particular publisher or author survives you, "completist" becomes a much more limited signifier. (This encompasses not only an author's physical, or a publisher's corporate, survival, but also the survival of material, the existence of which may be unknown at the time of your own demise.)
Ditto the applicability of completist re particular topics you may have been collecting, as such topics are likely to continue to generate literature after your demise.
As for material published during one's own lifetime, completist suggests only your side of the equation. It says nothing about the content-producing side of the equation: all those outlines and rough drafts and other fragments that an author left behind, for example, are by definition incomplete.
And what about all those books that have been knowingly published although they were unfinished at the time of their authors' respective deaths.
One could start with Kafka. None of Kafka's full-length novels were finished during his lifetime. In fact, Kafka's literary executor, Max Brod, had specific instructions from the author to burn all manuscripts that remained unpublished at the time of the author's death. That Brod ignored Kafka's instructions has proved to be something of a mixed blessing: The Castle, for example, stops mid-sentence. (Images below via Wikipedia:)
The longest epic poem in the English language (below left, via Classic Books & Ephemera) was only half-finished when Edmund Spenser died. The Mystery of Edwin Drood was only half-finished when Dickens died. Twain wrote three different versions of The Mysterious Stranger (below right, via Leura Books) over a twenty year period, none of which was finished at the time of his death. Balzac's La Comédie humaine was only 2/3 complete when that great French novelist died. Yet a completist thinks nothing of adding such unfinished titles to his or her shelves (because a literary executor and/or publisher somewhere, at some time, deemed the available material "fit to print":)
Interested in Hemingway? Although all three titles have been published, neither The Garden of Eden, nor Islands in the Stream, nor A Moveable Feast were finished at the time of the Nobel Laureate's suicide in 1962. Tolkien worked on The Silmarillion for decades, leaving the title unfinished at his death. Gogol died without finishing Dead Souls. Aquinas died without finishing his Summa Theologica. Marlowe died without finishing Hero and Leander.