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some_script.pl  file1  file2

  In a "while (<>)" loop, "eof" or "eof(ARGV)" can be used to
  detect the end of each file, "eof()" will only detect the end
  of the last file.  Examples: ...

my $prefix = 1;

...
    print "$prefix: $_";
    $prefix++ if ( eof );
}

  cat file1 file2 | some_script.pl

# or something less mundane:

  grep "target string" file1 | cat - file2 | some_script.pl

 echo "____STREAM_BOUNDARY____" > bndry
 grep "target string" file1 | cat - bndry file2 | script.pl