Sometimes, a mathematician dies suddenly, leaving behind very good mathematics that didn't make it through the publication pipeline. For example, it is possible they had a paper entirely ready to submit (maybe even already shared with their network, or on arxiv). Or they might even have submitted the paper and then died before the referee report came back (as referee reports seem to be taking longer and longer, this scenario is becoming increasingly likely, sadly). Rather than have important work hang around forever as unrefereed preprints, perhaps mathematical friends of the deceased would like to see their final work published.

What is the algorithm for getting the last paper of a recently deceased person published?

If the mathematician is a huge deal, someone might archive or publish their nachlass, as happened to Gauss. But that tends to happen more in other fields like philosophy, whereas I'm asking about submissions to normal math journals, where the paper would be reviewed by a professional mathematician and checked for correctness (and presumably someone, perhaps a student or co-author of the deceased, would make minor changes and corrections).

I know a few people have done this. For example, Georges Maltsiniotis has gotten a lot of Grothendieck's stuff published, including Pursuing Stacks. But I imagine some of this was contentious, and I imagine Maltsiniotis already gets too many emails about Grothendieck, so I figured I'd ask here instead of emailing him. A few examples of mathematicians who died suddenly in my field and left important mathematics behind are Bob Thomason, Jean-Louis Loday (I note that there are several preprints still on his webpage, and I believe his work with Vallette was finished after his death), Gaunce Lewis, Mark Steinberger, and Mark Mahowald (who, despite being 81 when he died, still had work in progress that was completed by his co-authors after his death) just to name a few.

I imagine someone has to get the rights to publish the paper. Do those normally pass to next of kin by default? What other steps are necessary that I'm not thinking of? Do people know of journals that have done this before?

Long term, I'd love to see a journal designed to publish papers of mathematicians who died before they could see their last works through the publication process. Depending on how much work was required to get the paper in shape, you can imagine partial credit going to a non-anonymous helper who corrected errors, rewrote proofs, added an introduction, etc. But I'm asking a simpler question now, about how to get it done in the current math publishing world. Because of the nature of the mathematical peer review process, I think this question is a better fit for MathOverflow than Academia.SE. A related but very different question was asked on MO last month.