local $SIG{__DIE__} = sub {
    open my $fh, '>>', 'log.err'
        or warn "Can't append to 'log.err': $!" and return;
    print $fh @_, "\n\$\@: |$@|";
};
eval { die "fubar!"; }; # <--- update, semicolon was missing
1 / 0;
__END__
Illegal division by zero at foo.pl line 8.