sub DESTROY
{
    my $output = `some_additional_cleanup 2>&1`;
    ...
}

##</code><code>##

my $obj = My::Object->new();
...
if ($!) {
   die "something bad happened: $!";
}

##</code><code>##

sub DESTROY
{
    local ($!, $?);
    my $output = `some_additional_cleanup 2>&1`;
    ...
}