Look at what my @flds = split '\|', $line; is doing with the lines whose last two fields are empty, e.g. |3104|1|New Years|Holiday|Clinic|||
Unfortunately, it does not return zero-length strings for trailing empty fields, as it ought to (and, I thought, used to).
Instead, it doesn't return them at all; @flds is shorter by two.
So you get undef when you try to access the fields at those indices.

If you don't want trailing empty values stripped, then use split '\|', $line, -1; as documented at split.

- tye        

Look at your output.

3104|1|New Years|12/31/2007
3104|1|Holiday|1/1/2008
3104|1|Clinic|1/2/2008
3104|1||1/3/2008
      ^^---- the uninitialized value is here
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You do

print "$PID|$SID|",shift(@flds),"|$date\n";
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print "$PID|$SID|",(@flds ? shift(@flds) : ''),"|$date\n";
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But if those output lines containing an empty 3^rd field are unwanted anyways, say

print "$PID|$SID|",shift(@flds),"|$date\n" if $flds[0];
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Why are you

my @dates_copy = @dates;
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copying @dates each pass through the loop? Just iterate over @dates.

_($_=" "x(1<<5)."?\n".q·/)Oo.  G°\        /
                              /\_¯/(q    /
----------------------------  \__(m.====·.(_("always off the crowd"))."·
");sub _{s./.($e="'Itrs `mnsgdq Gdbj O`qkdq")=~y/"-y/#-z/;$e.e && print}

Use of uninitialized value in print at xxx line yyy, <STDIN> line 2 (#
+1)
    (W uninitialized) An undefined value was used as if it were alread
+y
    defined.  It was interpreted as a "" or a 0, but maybe it was a mi
+stake.
    To suppress this warning assign a defined value to your variables.

    To help you figure out what was undefined, perl tells you what ope
+ration
    you used the undefined value in.  Note, however, that perl optimiz
+es your
    program and the operation displayed in the warning may not necessa
+rily
    appear literally in your program.  For example, "that $foo" is
    usually optimized into "that " . $foo, and the warning will refer 
+to
    the concatenation (.) operator, even though there is no . in your
    program.
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The problem occurs on the following line:

print "$PID|$SID|",shift(@flds),"|$date\n";
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To debug this, I changed this line to:

print shift(@flds),"\n";
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and I still get the warnings messages. This leads me to believe that you are trying to shift an element from an empty array.

@flds contains: 'New Years' Holiday Clinic

In other words, you've six dates and three fields. You're trying to print one field with each date, and there aren't enough fields to go around. So you get three undefs, one each for the final three shifts.

Try it like this:

use warnings;
use strict;

chomp( my @horiz = <STDIN> ); 

my @dates = grep length, split /\|/, shift @horiz; 

for my $line ( @horiz ) { 

    my ( undef, $PID, $SID, @flds ) = split /\|/, $line, -1; 

    for my $date ( @dates ) {
        print "$PID|$SID|", shift( @flds ), "|$date\n"; 
        } 
    }
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replace 

for my $date (@dates_copy) { 
print "$PID|$SID|",shift(@flds),"|$date\n"; 
} 

with


for my $date (@dates_copy) { 
    my $field = shift(@flds);
    $field = '' unless ( $field );
    print "$PID|$SID|",$field,"|$date\n"; 
}
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