I am a Masters student in math and thus new to academia and publishing in general. I am a coauthor on a number of recently submitted papers and had the (somewhat intrusive) thought, what happens to papers that get rejected? Of course, the simple answer is that they get corrected/improved based on referee reports and resubmitted somewhere else, but are there cases where papers simply never get published or stay in limbo forever? In these cases, what happens to the results/theorems/proofs they contain? (My question was also partially motivated by the fact that in one of our papers we cited a preprint from the 90s, which has been cited dozens of times but does not seem to have ever been published in a peer-reviewed journal.)
On the one hand, publishing in peer-reviewed journals is pretty difficult, and I'm sure papers are more often rejected than accepted. So there are bound to be papers that never end up making the cut. But on the other hand, looking at various researchers' academic websites, all of the papers in the "submitted" category seem to be pretty recent, suggesting that all of their submitted papers from before, say, three to four years ago ended up published. Or perhaps it is common to "silently" remove an in-limbo preprint from one's CV after a certain period of time?
I guess all of this is a long-winded way of asking: "What proportion of papers are eventually accepted?" Like I said, I'm in math, but answers regarding other fields would be interesting as well!