bug#39667: 26.2; Restarting a *shell* buffer breaks saving history

[ndame]

I tried it on windows.

Start M-x shell.

Check the value of comint-input-ring-file-name in the buffer. It's
"~/.history" and the input ring has values read from this file.

Exit the shell with Ctrl+D. The shell exits, the buffer remains.

Restart the shell with M-x shell.

Check the value of comint-input-ring-file-name. It's nil, because
comint-input-ring has already has a value from the previous
invocation, so shell-mode skips the whole history setup: (when
(ring-empty-p comint-input-ring) ...

Without the setup shell-write-history-on-exit is not called and if it
were it would do nothing, because comint-input-ring-file-name is nil.

Therefore the restarted *shell* buffer won't save commands made in it
to history.