Since you're using <$LOG> and not <LOG>, you could do the following:

use strict;
use warnings;

package MyPackage;

sub open_file {
   my $fh;
   my $ok;

   require 5.006;  # Require Perl 5.6

   # Support both 2 and 3 arg version of open.
   if (@_ == 1) {
      $ok = open($fh, $_[0]);
   } else {
      $ok = open($fh, $_[0], $_[1]);
   }

   die("$!\n") unless $ok;
   return $fh;
}

1;
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use strict;
use warnings;

use MyPackage;

our $LOG = open_file('log.txt');  # 'my' instead of 'our' also works
while (<$LOG>) { print; }
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Well, the logic to import open_file is missing, but that's easy. Check Exporter for details. Change open_file to MyPackage::open_file in the .pl until this is resolved.

Update: If you wanted to use <LOG>, how about:

use strict;
use warnings;

package MyPackage;

sub open_file {
   local *fh;
   my $ok;

   # Support both 2 and 3 arg version of open.
   if (@_ == 1) {
      $ok = open(*fh, $_[0]);
   } else {
      require 5.006;  # Require Perl 5.6
      $ok = open(*fh, $_[0], $_[1]);
   }

   die("$!\n") unless $ok;
   return *fh;
}

1;
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use strict;
use warnings;

use MyPackage;

*LOG = open_file('log.txt');
while (<LOG>) { print; }
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