OpenSSH support for signaling remote processes is rather limited and so goes for Net::OpenSSH.

The only way I know to get OpenSSH to kill the remote process when the local one is terminated is requesting a tty:

my ($in, $out, $pid) = $ssh->open2({tty => 1}, "tail -f /foo/bar");
...
kill TERM => $pid;
waitpid $pid, 0;
close $in;
close $out;
[download]

That may generate a harmless warning from OpenSSH ssh that you can ignore.