Steps to reproduce:

   emacs -Q -f eshell
   $ sleep 100 &
   $ kill -9 <sleep's process id>

After this, you'll see two Eshell prompts get emitted (one with a "[9]" 
for the exit status of "sleep"). We don't want to emit prompts when 
background processes die though.

This is a regression from Emacs 29, likely due to some changes I made to 
improve support for complex background commands. Eli, is this ok to 
merge to the release branch?