>>11308882
Making the placement exam humiliating has the unfortunate effect of harming free women as much as slaves...

>>11308877
If you don't mind me heading into the realm of urban fantasy, when I said placement exam, I actually almost imagined it as a sort of innate quality that's been sniffed out, like a gene or something like that.
One idea that's spinning around in my head is that it's related to magic. All men and most women gain the ability to use magic around puberty, almost invariably by 18 (no one has ever gained magic later than that). Failing to attain magic means one is "forsaken by god" and being enslaved. The average civilian isn't a powerful mage and is usually only capable of little puffs of smoke and such when they haven't dedicated themselves to training it, but the "forsaken" reject magic and have no sensitivity to it (though are subject to its effects still). It's easily possible to test for that magic, and such a test is administered at 18 to everyone (in order to make absolutely sure there's no latent magical potential that will be awakened). Through some strange quirk, only women can possibly be "forsaken".
In a society founded on magic, "forsaken" have nothing to offer, and such must be ritually enslaved. Perhaps we would even believe that it's right that we're enslaved. After all, otherwise we'd be worthless parasites - we must work in servitude to pay back our masters for allowing us to live in their world.
(I'd be happy to expand on the setting if there's interest!)