I was asked to review my own paper by a top field (i.e., JEEM) once, but this is different:
Eerily familiar”: That’s how Serdar Sayan of TOBB University of Economics and Technology in Turkey says it felt to read a submission to the Scandinavian Journal of Economics, after the journal asked him to review the manuscript. It turns out, it was Sayan’s paper, word for word, equation for equation, down to the last punctuation mark. But this wasn’t a case of authors faking email addresses for reviewers to rubber stamp their own work – instead, the author had plagiarized from a paper Sayan had published a few years earlier. Sayan describes the surreal experience in the Review of Social Economy (vol. 74, no. 1, 2016), in a paper titled: “Serving as a referee for your own paper: A dream come true or…?”
“I have been asked by a journal to serve as a referee for my own paper. Obviously, this sounds just as unlikely, and probably almost as intriguing, as saying ‘I have attended my own funeral.’” — Serdar Sayan, Review of Social Economy (vol. 74, no. 1, 2016)
I know people who won't publish working papers online for fear that people will steal their work (my comeback is that the working paper is the evidence that you got there first). The logical extension of that thinking is don't publish your papers in journals that have an online presence and here is evidence that is a good idea.