Taking the simplest interpretation of your problem description and modifying the sample data somewhat, the following may be what you want:

use warnings;
use strict;

my $start = '0020';
my $end = '0204';

my $data = join "", <DATA>;

pos ($data) = 0;
while (pos ($data) < length ($data))
  {
  last if $data !~ /\G.*?($start)/gis;
  my $begin = pos ($data);
  last if $data !~ /\G.*?($end)/gis;
  my $end = pos ($data) - length ($end);
  print ((substr $data, $begin, $end - $begin) . "\n");
  }
  
__DATA__
045a010000020000004c4553 4f4e4452412043414c4c4544 204241434b2c20492041
+4456
00020400 495345442054484154205745

prints:
000004c4553 4f4e4452412043414c4c4544 204241434b2c204920414456
00
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