No, not really. Economic constrains are the real issue. It makes no difference if a person decides to live spending less if he is never constrained by what he can afford. On the other hand, if someone needs something (say medical care) but can't afford it then there's a problem.
Minimalism doesn't really buy you a whole lot when just rent is already half of your paycheck, anyway. There likely just isn't much left to cut. The things I already own don't add to my cost of living, I already own them.
Conceptually possible, but in practice what market forces ensure that such a group exists?
I know a non-zero number of people that both work paycheck to paycheck and also make work the most important part of their lives. That's not to say it's mutually exclusive with 'neither' group, but I don't think it's impossible for the 'neither' group to shrivel into non-existence.