Yes, the $509 will continue to carry over until you get HDHP coverage again - which, of course, may be never.
However, as I pointed out, now that your HSA value has dropped to zero, there will be no penalty charged to you.
In the Review, TurboTax asks you to choose Self or Family for your HDHP coverage - however, you don't have any HDHP coverage.
But since you said that you did not have any HDHP coverage, the calculate of the annual HSA contribution limit will be correct. So don't worry about answering Self or Family, just to get around the gotcha in the Review. The numbers on your 8889 will be correct.
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