Never heard of anything like this in the U.S. "Unemployed" is normal and not considered derogatory. I've heard the euphemism "between jobs" but even that is rare. When I was unemployed, I went to the unemployment office to sign up for my unemployment insurance. I told my friends that I was "unemployed" or "out of a job" or "not working" or "had been let go." I had NEVER heard the phrase "unwaged" until I read this post. Perhaps you might share the name of your textbook with us? I'm curious...

Sounds like nonsense. We still use "unemployed" in Australia, without it being derogatory.

It IS untrue and nonsense. That is the whole point of so-called 'political correctness' - you end up having to say some ridiculous things in a pointless effort not to cause offence. I'm aware of the book you refer to and know the authors (in fact one of them is a close colleague of mine in Cambridge). And as Peachey points out, this is given is an example rather than a fact. The section is the book is explaining about the term 'political correctness' (and the fact that we use the term 'political correctness' in a mocking and derogatory way). As for the word 'unwaged', it does exist. You might come across it in government or official literature, or perhaps somewhere like a museum website, where they list the entrance fees and the categories of people eligible for a discount (eg senior citizens, under 16s, 'the unwaged'. But no, it isn't a word anyone would use in everyday speech, and yes, we can still say unemployed!

Untrue, Nonwaged sounds ridiculous

Googling on it, I get the impression that it is British. And that an important aspect of it is that it includes not just people who are unemployed, but people stay at home and do unpaid work keeping house or caring for children.