Thank you very much for the time you spent, and for your hint. I'll publish the script, just for reference, but I'm quite in a rush to have it running and I must first clean it of any sensible data. For now the fix seems to be this:

   if ($out =~/$last(.*)$/s
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and today is also the day I learnt what

   //m 
   //s 
   //ms
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are as modifiers. I never had a real need to think about these use cases so far and I had to study better the documentation. Thanks again UPDATE: here a snippet (it seems working now)

  1 #!/usr/bin/env perl
  2
  3 my $fileA = 'fileA.txt';   # the file to store incremental greps o
+n fileB
  4 my $fileB = 'fileB.txt';   # the live file which is log-rotated ev
+ery 10MB
  5 my $pattern = 'xxxx';
  6
  7 #--------------------------------
  8 sub main {
  9     $out = qx/grep -A 1 -B 1 $pattern $fileB/;
 10     $out && writeA (\$out);
 11 }
 12 #--------------------------------
 13 sub write_file {
 14     my ($file_name, $content_ref, $write_mod_append) = @_;
 15     my $write_mod = $write_mod_append ? '>>' : '>';
 16     open(my $fh, $write_mod, $file_name) or die "Could not open fi
+le '$file_name' $!";
 17     print $fh $$content_ref;
 18     close $fh;
 19 }
 20 #--------------------------------
 21 sub writeA {
 22     my ($out_ref) = @_;
 23     my $write_mod_append;
 24     if ( -e $fileA ) {
 25         $write_mod_append = 1;
 26         my $last_line = qx/tail -1 $fileA/;
 27         chomp $last_line;
 28
 29         if ($$out_ref =~/$last_line(.*)$/s) {
 30             $$out_ref = $1
 31         }
 32     }
 33     write_file ($fileA, $out_ref, $write_mod_append) if ($$out_ref
+ =~ /\S/);
 34 }
 35 #--------------------------------
 36 main;
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where a live fileB is for example this:

--------------...------------
--------------...------------
--------------aaa------------
-------------xxxx------------
--------------bbb------------
--------------...------------
--------------...------------
--------------ccc------------
-------------xxxx------------
--------------ddd------------
--------------...------------
[download]

A first grep -A 1 -B 1 $pattern $fileB will be saved as fileA

--------------aaa------------
-------------xxxx------------
--------------bbb------------
--
--
--------------ccc------------
-------------xxxx------------
--------------ddd------------
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After some time fileB can contain some more data (it's a live log) or it can be completely overwritten (log rotated on itself after 10MB)

--------------...------------
--------------...------------
--------------aaa------------
-------------xxxx------------
--------------bbb------------
--------------...------------
--------------...------------
--------------ccc------------
-------------xxxx------------
--------------ddd------------
--------------...------------
--------------...------------
--------------eee------------
-------------xxxx------------
--------------fff------------
--------------...------------
[download]

A second grep -A 1 -B 1 $pattern $fileB, will find 3 occurrences, but actually the <NEW> one is only the last xxxx. If I'd then append the grep output as it is, I will have 2 duplicates. I cannot just overwrite fileA, because when B is log rotated, the previous greps would be lost, not stored in my incremental fileA which should look like:

--------------aaa------------
-------------xxxx------------
--------------bbb------------
--
--
--------------ccc------------
-------------xxxx------------
--------------ddd------------
--
--
--------------eee------------
-------------xxxx------------
--------------fff------------
[download]