It always boggles my mind that losing socks in the laundry is such a common phenomenon. A socket is either collected, or left in the machine. There's nowhere else it could go. It's not like a tape measure or a pen that carried around house and could be put somewhere without you consciously registering it. Maybe some washing machines have really strange geometry that is prone to conceal socks?
I have, however, just settled on a uniform for work: same underwear, white or black socks, grey t-shirt under my scrubs (oh, the joys of wearing pajamas at work). Darn Tough socks aren’t cheap, but they are guaranteed for life, and they’re great for preventing smelly feet if you’re prone to them.
Now that you mentioned pets, it makes perfect sense to me.
My cat has indeed never been interested in socks. However, he'll move almost everything else. I still remember the day I had to wear sun glasses to classes, because he hid my normal glasses, later discovered to be behind the bookcase.