I don't think it's a good idea to open and close the file to write to each time. I'd initialize a hash with the year as key and the handle as value, opening a new one if none exists in the hash for that particular year. To keep things clean I'd use IO::File.

Also, but this is minor, I'd not use the substr since this is waste of time: $line =~ /^[0-9]{9}/ should do nicely as condition to keep the line.

Just my 2 cents, -gjb-

You are opening and closing a file each time through the loop when the year isn't '02'. This could be a significant impact on your runtime if there are a lot of these records. It might be best to establish a hash of file handles and keep them open. Something like this (untested):

my %handles;
my %count;
sub get_file_handle {
    my $yr = shift;
    $count{$yr}++;
    return $handles{$yr} if exists $handles{$yr};
    $handles{$yr} = IO::File ">>".$path."year$yr.txt";
}
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I don't know what your OUTPUT handle is assigned to. If you put it in the hash with the key '02', you could remove the if ($year...) test inside your loop. Then, your valid line handling becomes:

   print get_file_handle($year) "$newline\n";
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You do a chomp on the record read from the file only to add a newline when you print to output. If the removal of the newline is not required by your validLine() routine, get rid of both.

---
print map { my ($m)=1<<hex($_)&11?' ':'';
$m.=substr('AHJPacehklnorstu',hex($_),1) }
split //,'2fde0abe76c36c914586c';
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Except that will have to read print { get_file_handle($year) } "$newline\n";

$ perl -le'sub x { \*STDOUT }; print x() "blah"'
String found where operator expected at -e line 1, near ") "blah""
        (Missing operator before "blah"?)
syntax error at -e line 1, near ") "blah""
Execution of -e aborted due to compilation errors.
$ perl -le'sub x { \*STDOUT }; print { x() } "blah"'
blah
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Makeshifts last the longest.

You are chomping the line, even though you never look at anything other than the first record on the line if its not valid, then catenate a newline back to the end of it on saving it. You repeatedly open/close files for single records. Your regex has a quantifier of {9} although you already made sure only to look at the first nine characters - a double negative is more economic in that case (test for the absence of non-digit characters).

Also, you can reduce quite a lot of duplication.

my (%handle, $fh, $count);
$handle{02} = \*OUTPUT;

while(my $line = <INPUT>) {
    if(substr($_, 0, 9) !~ /\D/) {
        chomp $line;

        my $year;
        ($line, $year) = validLine($_);
        $line .= "\n";

        $count = $year ne "02" ? \$y_count : \$o_count;
        $fh = $handle{$year} || do {
            open my($newfh), ">>", $path."year$year.txt"
                or die "Cannot open file: $!\n";
            $newfh;
        };
    }
    else {
        $fh = \*DISCARD;
        $count = \$d_count;
    }
      
    ++$$count;
    print $fh $line;
}
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Makeshifts last the longest.