This is exactly the pointer (pun intended :) I was looking for.

The following code accomplishes my task:

#!/usr/bin/perl -T

use strict;
use warnings;

use Devel::Pointer;

eval {
    require('some_code.pl');
};
if ($@) {
    my $start = index($@, 'HASH(0x') + 7;
    my $end   = index($@, ')', $start);
    my $hex   = substr($@, $start, $end-$start);
    my $addr  = hex($hex);
    my $href  = unsmash_hv(0+$addr);

    print("$$href{'Error data'}\n");
}

# EOF
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Since the hash is guaranteed (in my case) to have a non-zero reference count, this code is safe for my purposes.