There's a photo going viral on Twitter that supposedly shows what happened when a landlord removed the bottom panel from one of the washing machines in her building. There's a compartment down there . . . and it's PACKED with socks.
Is it possible that all of your missing socks are trapped in a hidden compartment in the bottom of your machine? Well, maybe.
If you have an older washing machine and dryer, it could be worth opening it up to take a look. But newer machines are made a little tighter, so there isn't space for things to fall through the cracks.