Hummm .... your question chimes in with some thinking I've been doing about political alternatives.
I think there is an underclass. And I think the definition of this underclass could be something like ...
... the underclass consists of people that have no economic power or economic equality, due to the fact that their skill set is perceived to have little value in a particular set of economic circumstances, and, as such, they are unable to trade their labour for goods and services, even if they should wish to do so.
This, I think, provides a more lucid insight, even though, I admit, my definition has flaws: the underclass are unable to trade their labour, while the working class are able to trade their labour (even if, sometimes, they don't want to, and maybe are not at the present time).
Then, if you look at why these people are unable to trade their labour, you then allow space for a spectrum of circumstances: they are skilled in un-economical viable forms of labour (either down to technological advances or geographical economic change, say), or they never had any economically viable skills in the first place, or they cannot trade their skills due to ill-health etc.
So then, when you consider a hypothetical situation where 1000s jobs suddenly appeared in an area where those jobs cross a wide range of skillsets, the working class people are the unemployed people that could and would be employed, whereas the underclass unemployed would still have nothing to offer -- unless they acquired the relevant economically viable skills.
This gives a definition of the underclass as a group that would fail to be employed even in a climate of full employment (within a particular paradigm of economic activity, mind).
Mibbe.
This is just a rough thought, mind. Feel free to disagree all you want.