The new open access online journal Rejecta Mathematica accepts only papers that have been rejected by other journals. (I can’t quite work it out now, but it seems that an inconsistency caused by a semantic or set theoretic paradox may lurk somewhere in the works.)
The journal’s about page anticipates that submissions may include papers which are simply too long to have been properly assessed, those whose subject matter lay outside of the competence of reviewer of journals to which they’d been previously submitted, those with serious technical flaws which may nonetheless be interesting for other reasons , those in which already known results are proved in novel ways and, of course, papers which include plain old crack-pot rants against the publishing hierarchy.
The motto of the journal is caveat emptor (“let the buyer — downloader — beware”) which is a clever shorthand way of indicating that submissions aren’t peer reviewed but rather only merely “peer skimmed”, supposedly to make certain that they have something to do with some sort of vaguely mainstream area of current mathematics research.
Perhaps PhilPapers could have a collection of papers each of which had been similarly rejected by philosophy journals…