Re: Swisscare - big trouble
What I would do is to sort out her registration as soon as possible with a legitimate residency permit and address. Use that info to sign up for any basic health insurance policy, and declare a back-dated time of entry which can be up to 3 months prior, and hopefully it will all work out.
Otherwise, you're paying out of pocket for your health bills. Did swisscare at least refund your premiums because they refused to pay your cover ?