How can one still become wealthy despite unforeseen financial hardships?

How can one become financially independent when his/her savings, middle class earning, and assets are being devoured and are wiped out by paying medical bills that HMO insurance will not cover and he/she is barely getting by on paying for the bare necessities and have given up on cell phones, home internet service, and cable/satellte?

Although I am blessed with so far not having to deal with these financial/health issues. However, as much sa as I do prepare for the worse, especially eliminating all non-mortgage debt, I will like to know how can one prosper after the unexpected worse happens. Unfortunately bad things do happen to good people and live goes on no matter what.
Small (or big world), for the answere you mentioned Dave Ramsey, I just passed a billboard advertising his show here in Atlanta. I’ll check him out .Thanks!