Class is not a thing but a relation. Income is irrelevant except when it is a disguised from of participation in surplus value. Not a very interesting member of the working class, but still a member of it, insofar as she is constituted by her relation to capital, which is constituted by its relation to her. Read Bertell Ollman. Class is a process, a complex of relations, not a thing, not a box into which you toss cubes.
Class makes no sense except as a complex of internal relations of capitalism.