I wish these machines would just stay slightly open when off. I leave mine open when it's not in use and haven't had an issue. If it makes you feel any better, our cats have never gone inside the washer. They're much more interested in sneaking behind the machine.
I will note that when I forget and leave clothes after a wash for more than a day, they do get a slight mildew smell. The same thing happens with the top loader at my in-laws. Another wash gets rid of it in both cases.