Since the Brexit vote it became widely known that, as an EEA citizen, to obtain a Permanent Residence in the UK you either have to be in the Worker or Self-Employed categories. If you are "only" a Student or Self-Sufficient, then you not only need to live in the country for five years to be eligible, but you also need to have Comprehensive Sickness Insurance (CSI).
Apparently based on multiple sources if you're a British citizen, and you have an EEA citizen partner, who is either a Student or Self-Sufficient, then they need to have CSI, otherwise they won't be able to obtain a PR, even if you yourself are working.
However I couldn't really find a definite answer on what happens if you are a non-British EEA citizen, who is working (so doesn't need CSI), whether your partner would still need to have CSI, or whether the fact that you are working covers them in this regard. The application form for PR seems to imply that you working is enough, but that looks a bit weird, because if I would be a British citizen it wouldn't.