| Yes it can be done, but in order to make sure that everything gets favorable tax status I suggest you get professional help (a lawyer or accountant who knows how to set these things up).
A properly done reverse mortgage has no tax implications as the money is taken out, the interest is deductible by the estate. Also, the money needed to repay the loan upon your parent's death means that there is less money in the estate that is subject to estate tax as well (though this sounds like it's not an issue, at least federally for you). Of course, you will have to pay taxes on the interest.
A few questions: How old are both of your parents? How likely are they likely to continue to live in the coop? What is the coop worth? You say they have a large tax bill? From what? Are they likely to have futher tax problems? | 
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