The documentation for Tie::STDERR is a little sparse, so I used tie_stderr.t. Try this:

#!/usr/bin/perl

use strict;
use warnings;

BEGIN { $|=1; }
END   { print "not ok\n" unless $::tiestderrloaded; }

BEGIN { print "Loading Tie::STDERR\n"; }

use Tie::STDERR \&HandleError;
$::tiestderrloaded = 1;

print "Before\n"; 
if ($@) {
    die "....";
}  
print "After\n";

use Tie::STDERR undef;

sub HandleError { 
    my ($error) = @_;
    &SomeActivity('0',$error);
}

sub SomeActivity {
    my ($rc, $error) = @_;
    print $rc . "\n" . $error; 
}
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