Where do bad papers go to die? After a paper is rejected several times by several journals it begins to become clear that the research was off the mark no matter how much editing, fixing, and revisions are done. Therefore,

What do scholars do with unpublishable papers? 

Do they stick them in a file drawer and pretend it never happened? Perhaps they burn them? Or do they try to pull something from the ashes for another paper. It's somewhat depressing to spend months on a project to watch it murdered during the review process. Surely there is some sort of afterlife for a rejected article?
There's always room to publish any paper, even a computer-generated one that doesn't make sense. You just need to target the "appropriate" publication/venue.

Being more serious now, I have rarely seen any rejected work that "just died". For good or bad, the paper or parts of it were always later reused / resubmitted and eventually accepted.

I am not saying that's a good thing, because some papers/ideas/research topics are really terrible and absurd, but too many researchers are usually too stubborn / invested to accept it. Many of them, in fact, have made a career out of this (like republishing the same absurd/non-working idea for decades) and everyone seems to be okay with it.

These days there's really room for everything: publishing is a huge business. Again, it all depends on your standards.