There did exist a means through which one could escape the shackles of slavery, but from the documentation I saw the rules were incredibly strict. For starters, the master had to approve it, then the slave had to prove they had abilities worthy of leaving servitude. There was also a set fee that had to be paid to the clan in which the slave resided. It was a head-scratching piece of legislature if only for the fact it seemed to make escape impossible.
In present day Japan such legislature would result in criticisms, protests, and revolt, but alas this was a different world entirely. This was a place with an entirely different culture in which slavery hada well-established history, and so very few-if any-thought it unfair or abnormal.
Karen is much less naive than a lot of people, but this is very, very telling about her upbringing in both Japan and Falkrum, and also the kind of person she is. She learns information to benefit her current situation, but doesn't really look into cultural or historical affairs otherwise, and I think that's a weak point of hers in geopolitics. If she had any curiosity about world history in her last life, her first reaction would be "oh, this reminds me of the slave trade in the Americas".
I had the same sense when she described Ern as "not from Japan" (nor did she state her actual religion) way back in volume one. Ern had a terrible old life and so the information about what country she was from wasn't important information for Karen, just the basics of her death, because in Karen's mind, Ern's shitty life/death and where she was from weren't really related, at least considering their current circumstances. But to someone like me, they're absolutely related, and it's odd to think of someone's life divorced from them. For instance, it's very obvious the Ern lost her faith (or at least the appearance thereof) at some point, but Karen doesn't discuss this.
(There's also the Doylesian view that the author didn't want to state the country and religion to avoid making any nation/religion look bad, but they definitely did it in a way that helps you get a sense of Karen's character.)