That probably means that on line 14 in your data file the regular expression does not match the data.

Secondly, you can test the result of the match to verify that you really got 19 values out:

my $result =
(($beginning, $agency, $district, $ssn, $serv_per_m,
  $serv_per_y, $serv_per_t, $last_name, $first_name_i,
  $middle_name_i, $cover_group, $pay_code, $pay_rate,
  $earnings, $holder, $ret_percent, $surv_ben,
  $work_sch_code, $cont_amt, $cont_code, $stuff) =
  /
    (\d)      # $beginning
    (\d{4})   # $agency
    (\d{3})   # $district
    (\d{9})   # $ssn
    (\d{2})   # $serv_per_m
    (\d{2})   # $serv_per_y
    (\d)      # $serv_per_t
    (\D{10})  # $last_name
    (\D)      # $first_name_i
    (\D)      # $middle_name_i
    (\d{5})   # $cover_group
    (\d{2})   # $pay_code
    (\d{8})   # $pay_rate
    (\d{6}\D) # $earnings
    (\s{8})   # $holder
    (\d{4})   # $ret_percent
    (\d{3})   # $surv_ben
    (\d{3})   # $work_sch_code
    (\d{5}\D) # $cont_amt
    (\d{2})   # $cont_code
    (.*\s)    # $stuff
    $
  /x
);

if ($result == 21) {
  # Test the variables
} else {
  # This line did not match
}
[download]

It appears highly likely that you have a non-matching part of the regex that results in an undefined value some of the time. I would use something like code below to debug things. This assigns all of the individual var names into one array (@result) and avoids a mess with specifying each var name.

Run this on your data set and you see what it matching and what is not. Undefined is a "value" and I don't think that just checking scalar @result is enough. Anyway this should show where the program is failing to match, presumably on line 14 of the input.

my @result =   # note @ variable not $variable !!
(($beginning, $agency, $district, $ssn, $serv_per_m,
  $serv_per_y, $serv_per_t,.............);

while (<IN>)
{

   print;
   my @result = (.....blah) #see previous posters code
   my $token_nr=0;
   foreach my $token (@result)
   {
       $token_nr++;
       if (defined ($token) )            #if you try to print an undef
       {                                 #program will bomb
          print "$token_nr++\t$token\n"; #this allows you to see exact
+ly
       }                                 #what is undef without progra
+m
       else                              #bombing
       {
          print "$token_nr++\tUNDEFINED\n";
       }
   }
}
[download]

I suspect that your regex is too restrictive. Also fixed column files aren't that common but you may indeed have one. (\D) matches exactly one non-digit charater, to allow say somewhere between 1 and 4 non-digit characters, use (\D{1,4}). for a character set, use say  ([\d-]{9,11}) if ssn could be either 123-45-6789 or 123456789. Use \s* to indidicate zero or more space characters.

That regex won't produce undef for one of the captures only some of the time - the match is failing, so all the variables are presumably undef.
--
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Anyway, since you have some sort of error-trapping already in place, and you are getting errors that seem to indicate unexpected features in the input data, your next step should be to do some more elaborate checking for data that doesn't match the expected pattern.

It'll be easier if you create a list of field names, and use a hash with those field names as keys:

# assuming a row of data in $_, and row number == $.

my @fld_names = qw(
    begin agency district ssn serv_per_m serv_per_y serv_per_t
    last_name first_name middle_name cover_group pay_code pay_rate
    earnings holder ret_pcnt surv_ben work_sch cont_amt cont_code stuf
+f
    );

my @fld_types = qw(
    \d \d+ \d+ \d+ \d+ \d+ \d
    \D+ \D \D \d+ \d+ \d+
    \d+\D \s+ \d+ \d+ \d+ \d+\D \d+ .*
    );

my @fld_vals = (
    /(.)(....)(...)(.{9})(..)(..)(.)
      (.{10})(.)(.)(.{5})(..)(.{8})
      (.{7})(.{8})(....)(...)(...)(.{6})(..)(.*)/x );

# now do some testing of values...
for my $i ( 0 .. $#fld_names ) {
    if ( $fld_vals[$i] !~ /^ $fld_types[$i] $/x ) {
        warn sprintf( "Data row %d: bad value in field %d (%s): %s\n",
                       $., $i, $fld_names[$i], $fld_vals[$i] );
    }
}

my %fields;
@fields{@fld_names} = @fld_vals;
[download]

BTW, you need to learn to put <c> ... </c> around code and data when you post -- you can update the OP to add these tags, so that the code is readable.