[This is a corrected version of email I mistakenly sent elsewhere.]

 > I don't think the manual states that output can
 > arrive after the process has finished, but if that's the case, then it
 > should do so.

Good point, and I installed the attached patch into emacs-26 to try to do that.

As this bug report seems to stem from a misunderstanding of 
accept-process-output (quite understandable, as its functionality is obscure) 
I'm taking the liberty of closing the report. If I'm wrong please feel free to 
reopen it.