No. In order to contribute to health savings account (HSA), you must be enrolled in a high deductible health plan (HDHP) and you can't be enrolled in any of these other health plans:
- An employer-sponsored health policy that is not an HDHP
- A health FSA (whether yours or your spouse’s)
However, you can have insurance that provides benefits for:
- A specific disease or illness.
- A fixed amount per day (or other period) of hospitalization.
- Liabilities suffered under workers' compensation laws, tort liabilities, or liabilities related to ownership or use of property.
- VA benefits for hospital care or medical services for a service-related disability.
- Note: There are special rules for this situation.
You're also allowed to have coverage, provided through insurance or otherwise, for:
- Dental care
- Vision care
- Long-term care
If you had an HSA when you lost HDHP coverage, then you're still eligible to keep the HSA. You're just not eligible to contribute to it. You can continue to pay for qualified medical expenses until the HSA's funds are exhausted.