After my Dad passed, State took stocks for my Mom's care while in nursing home on Medicare. Is this a loss on my taxes?

It's not a capital loss for anybody. If south Dakota acquired these as a Medicaid Estate Recovery Program (MERP), they should never have gone to the daughters. That's why you need a lawyer to do Probate without errors.

Was it actually a loss in terms of a capital loss? I.e., have you figured the basis of the stock, checked the share price on the date the stock was surrendered, and calculated whether it was a gain or actually a loss?

As FF states, this would be a question for a CPA, but you could prepare for the meeting by doing this research ahead of time.

It might, e.g., be that the $28K would be considered a medical expense that could be deducted (assuming it exceeds 7.5% but you'll have to check on that as well as I believe it changes in 2016) of adjusted gross income, and any gain or loss beyond that would be addressed in Sch. D of your mother's tax return.

Who calculated that the stocks were worth $28K?

I'm assuming though that the stocks were titled in her name only?

You would need to check with a CPA or Accountant to see if that stock could be treated as health care expense or better to use as a stock loss.