As Eliya already stated, you weren't accurately creating a hidden field.

It's also important to note that if you want to capture the previous value of OldBugText, then you're going to have to save it in a temporary variable since you want to overwrite it each time as well. Something like the following is probably what you're aiming for:

#!/usr/bin/perl -wT

use CGI;
use CGI::Carp qw(fatalsToBrowser warningsToBrowser);

use strict;
use warnings;

my $q = CGI->new;

my $prev = $q->param('OldBugText'); $prev = '' if ! defined $prev;
$q->param('OldBugText' => $q->param('BugText'));

print $q->header;
print $q->start_html("Problem demo");
print "<h1>Problem demo</h1>\n";
print $q->start_form;
print $q->hidden(-name => "OldBugText");
print "<p>Previous Value: ", $q->escapeHTML($prev), "</p>";
print "<p>", $q->textarea(
    -name    => 'BugText',
    -value   => "Example Text",
    -rows    => 10,
    -columns => 40
), "</p>";
print "<p>", $q->submit('Action', 'Submit'), "</p>";
print $q->end_form;
print "<hr>\n";
print $q->end_html;

1;

__END__
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