use strict;
use warnings;
use Try::Tiny;

$SIG{__DIE__} = sub
{
    chomp(my $item = shift);
    print STDERR "DIE ERROR: $item\n";
    exit 2;
};

# ... code here ...

my $last_sig_die = $SIG{__DIE__};   # Save current setting
$SIG{__DIE__} = 'DEFAULT';

try
{
    die 'Dying';
}
catch
{
    print STDERR $_;                # Note: $_, not $@
};

$SIG{__DIE__} = $last_sig_die;      # Restore setting

die 'Really dying';