It means that those women live in a corrupt society.
It does not mean that those women are corrupt.

(I welcome the corrections or input of a native speaker!) it doesn't seem like the most natural or meaningful sentence, but it would seem to mean that these women (ele) live their lives deeply embedded in a state of corruption, that probably dictates not only their actions but those of the people around them. to be more clear, one could certainly have said, "sistemul lor e corupt" or that "ele sunt corupte" to make it a bit more clear, but I think the authors were creating a simple sentence that would use the noun coruptie, and not the adjective corupt.

I'm also wondering this: can the verb "a trai" be used like an emphatic form of the verb to be? That works in Latin: "vivis molesta" (you LIVE annoying) is a strong way of saying you ARE annoying. can this work the same? So, Ele trăiesc în corupție would then mean "they're very corrupt"?