To jarat44: Your question appears to be more of an insurance process question than a tax question. I will provide basic ideas in hopes that it might help you to move forward. But please remember that this forum is for tax questions--not for insurance problems.
With regard to taxes, I can say that the taxpayer is supposed to be the responsible party for their own insurance, the insurance for their spouse, and insurance for any dependent on their tax return. The insurance subsidy is based upon an initial estimate of income. Once one gets the subsidy, then they must balance their account with their 1095A at the end of the year. At the end of the year, the actual income is compared to the estimated income. The Form 1095A reports the subsidy numbers. If the subsidy is too low, one gets extra money added to their return. But if the subsidy was too high, then the government takes some back to put the account in balance. It's a relatively simple process if everybody follows the rules.
So back to the insurance question. I don't believe that anybody should be buying government subsidized insurance in your name if you are not included on their tax return. For initial steps, it appears that you will need to talk with your sister. You need to know all the details, and you don't want to be guessing about important details. If you are not your sister's dependent, then I don't understand why she would get subsidized insurance in your name. After, knowing all the details, I suggest talking to the insurance company to explain what happened and see if they have a process for this case. Try checking the contact information provided at HealthCare.gov 1-800-318-2596. Perhaps they have the procedures for this case.
