This would be a good place to use at least 'qr' (see perlop) or possibly the '/o' regex modifier (see perlre):

my $re = qr/$request/i;
my $i = my $g = 0;
for my $line (@array) {
 chomp;
 if ($line =~ $re) {
  #do stuff
  print $line, $email[$i];
  $g++;
 }
} continue { $i++ }
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