* test/lisp/eshell/esh-proc-tests.el (esh-proc-test/kill-pipeline):
Add pattern matching output when killing a process on macOS (and
possibly other BSDs).
* lisp/eshell/esh-proc.el (eshell-kill-process-function): Only reset
the prompt if PROC is writing to the terminal.
(eshell-sentinel): Only write the exit message if PROC is writing to
the terminal (bug#54136).
* test/lisp/eshell/esh-proc-tests.el (esh-proc-test/kill-pipeline)
(esh-proc-test/kill-pipeline-head)
(esh-proc-test/kill-background-process): New tests.
* lisp/eshell/esh-io.el (eshell-pipe-broken): New error.
(eshell-output-object-to-target): Signal 'eshell-pipe-broken' if the
target is an exited/signaled process.
* lisp/eshell/esh-proc.el (eshell-insertion-filter): Handle
'eshell-pipe-broken'.
* test/lisp/eshell/esh-proc-tests.el: New test.