That can create empty files. Fix:

while there's a next line
    extract the ID
    check if ID matches the previous ID
    if not:
        set previous ID to current ID
        increment a counter
        if counter > 100
            close current output file
            reset counter
    
    if output file isn't open
        open a new output file

    write the line to the current output file.
[download]

It can also create files with more than 100 records. Fix:

my $last_id;
my @group;
my $fh;
my $line_counter = 0;
my $file_counter = 0;

sub output {
    if ($line_counter + @group > 100) {
        $fh = undef;
        $line_counter = 0;            
    }

    if (!defined($fh)) {
        my $fn = sprintf('file%04d', $file_counter++);
        open($fh, '>', $fn)
            or die("Error create file $fn: $!\n");
    }

    $line_counter += @group;
    print($fh splice(@group));
}

while (<>) {
    my ($id) = /^(\S+)/;
    $last_id = $id if !defined($last_id);

    if ($id eq $last_id) {
        push @group, $_;
    } else {
        output();
    }
}

output() if @group;
[download]

If there's more than 100 record for one id, it'll put them in the same file despite the limit.

Note that both my code and the parent's pseudocode assume that the records are grouped by id in the input file.