Can your health insurance company raise your rates after you get sick?

I've heard about pre-existing conditions and all, but what about getting seriously ill AFTER you have insurance? Let's say you're generally healthy, and already have heath insurance which you pay for yourself, at a reasonable rate. Then you get a long term illness, or get into a terrible accident, and need years of expensive care. Of course you keep your policy up to date... Can the company raise your rates by triple (or worse) if you get sick this way?
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If you're covered by GROUP insurance (through your employer, for example), your rates will NOT be raised simply because you got sick or injured. Those rates are based upon the group and while they may go up each year, they will NOT go up specifically for you. However, if you have an individual policy, your rates could possibly be increased if you have an influx of claims. Unlike someone above me said, this is EXACTLY like car insurance. Your car insurance (which is an individual policy) is likely to go up if you have a large claim. Same thing is true of individual medical coverage. It's just a sad fact of life. When you're not part of a group plan, you are shouldering all the risk yourself. So if you incur a lot of charges, you may very well see an increase.
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