You’re correct in wondering whether health insurance companies can drop you because just a couple of years ago, it was common for providers to stop covering customers once they got sick – something the insurers called “rescissions.” They would look for and exploit technical errors on your application in order to make the case that your claims were fraudulent or simply require that you sign forms giving them the right to curtail coverage at their discretion.
Things have changed, however, following the implementation of the Affordable Care Act of 2010, which contains a provision prohibiting health insurance companies from dropping you due to honest application errors. While this provision legally applies to policy years beginning on or after September 23, 2010, the health insurance companies agreed to apply it starting in May 2010, following negative press coverage over the insurance company WellPoint allegedly targeting breast cancer patients for rescission.
With that being said, insurance companies can still drop you if: 1) you intentionally use false information on your application or 2) fail to pay your premiums. If they choose to do so, they must provide you with 30 days' notice, giving you time to either appeal the decision or look for a new provider so that your coverage does not lapse.