Just make opening the file conditional on the array holding at least one value:

if ( scalar @matches ) {
    make_path($parsed_dir);
    open my $out_fh, '>',
        "$parsed_dir/${basename}.$wanted.$rnumber.txt" or die $!;
    print $out_fh $_ for @matches;
    print $out_fh "\n";
    close $out_fh;
}
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Also note the addition of or die $! to your open() call -- always a good idea to check whether it succeeded.

Hope this helps!