Paperbacks without covers are stripped books (hat tip user14111). The Economics of the Publishing and Information Industries: The Search for Yield in a Disintermediated World has a pretty good explanation of why they exist:
All books can be returned for a full refund as long as the basic (and publically announced) terms and conditions of sale are followed. Returns are a blight on book publishing since a book sold today can be returned tomorrow, which makes planning, especially in the short term, exceptionally difficult. Problems in estimating the proper market for a book, uncertainty in the marketplace, and inefficiencies in the channels of distribution contribute to this serious problem. A book can be returned for full credit (in essence, this is a consignment sale) to the publisher as long as clearly promulgated terms of sale conditions are followed. In some instances, a bookstore or distributor has up to two years to return a title. The entire hardbound book (including the dust jacket) is returned; however, a trade or mass market paperback is stripped of its cover and only the coer is returned. The remaining stripped book is supposed to be pulped, although some street merchants in many major cities obtain (almost certainly illegally) and sell stripped books, for a fraction of the suggested retail price.
There's a pretty good argument that this practice is wasteful. This blog posts in Publisher's Weekly makes the argument that if you aren't going to sell the book, then there's no reason why you can't give it away for free to someone living in a book desert. (Credit to Gallifreyan to linking to the tweet that linked to the Publisher's Weekly article).
As Rand suggested in a comment, this answer might be a good place to explain how to use search engines to find reputable sources. In the comments, someone mentioned that "Sometimes you just get lucky with your search terms." The thing about luck is that when you need it you don't have it. Relying on luck is not an effective research strategy. Let me describe my strategy for researching this question, which as you will see, relies not on luck but on persistence.
To find Economics of the Publishing and Information Industries, I used two separate search engines: Google and Google Scholar. Google Scholar is a version of Google that only indexes academic resources (e.g. books or journal articles). Since academics tend to cite sources, academic sources are almost always, but not always, more reliable.
From a comment/now deleted answer from user14111, I learned that the term for a book that is missing its cover is a "stripped book." I started my research by Googling the term "stripped book," but I did not get any results other than the Wikipedia article that user14111's now deleted answer cited. Since Wikipedia is not a reputable source, and since the Wikipedia article did not cite any sources for its definition of stripped books, I kept searching.
I then tried using Google Scholar to search for the phrase "stripped books". I did not find any results. I knew then that the keyword "stripped books" was too broad, and that I needed to narrow it down. Thinking that "stripped books" were a practice of the publishing industry, I tried "stripped books publishing" in a normal Google search. I still didn't get any results. I then reasoned that this was a question about the business practices of the publishing industry. I then added the keyword "economics" to make the query "stripped books publishing economics". And I finally found The Economics of the Publishing and Information Industries, which was the fourth result of my query. If I hadn't found it then, I would have kept trying different queries. I don't select queries at random, usually, my strategy for search keywords is to be as specific as possible.
No luck is involved. It's just persistence and a little bit of skills and experience.