She does not work at all, I provide for her, and she lives with me the whole year. But she has insurance through her parent's government insurance and they live in another state.
Who pays for her health insurance does not determine if she can be claimed as a dependent.
If she meets all the requirements under the Qualifying Relative rules then you can claim her as a dependent on your tax return.
To be a Qualifying Relative -
1. The person cannot be your qualifying child or the qualifying child of any other taxpayer. A child is not the qualifying child of any other taxpayer if the child's parent (or any other person for whom the child is defined as a qualifying child) is not required to file an income tax return or files an income tax return only to get a refund on income tax withheld.
2. The person either (a) must be related to you or (b) must live with you all year as a member of your household.
3. The person's gross income for the year must be less than $4,200 (social security does not count) in 2019
4. You must provide more than half of the person's total support for the year.
5. The person must be a U.S. citizen or a U.S., Canada, or Mexico resident for some part of the year.
6. The person must not file a joint return with their spouse.
Since the issue is "do you pay more than half the person's total support", you would have to evaluate the cost of insurance as being a support cost paid by the parents, along with any other support provided by the parents; then evaluate any other sources of support (state benefits, welfare, section 8, etc); and the support provided by you; and add up whether you provide more than half.
An adult partner is never a qualifying person for head of household status, even if they are a dependent. You would need to be claiming at least one other dependent who is a qualifying person for HOH, usually your biological or adopted child.