Q. Can we claim her keep (room and board) as a medical expense we pay on behalf of the parents?
A. No. Your sister is not a medical professional. Even if you could, you could not count "room" at all, as it is not out of pocket. You would have to track food expenses, and even that is iffy. Your sister would have to report the income as self employment income, paying social security and medicare tax in addition to income tax. Your deduction would be limited by the 7.5% rule and itemizing.
Claiming the dependent care credit might be a possibility, if your parents are your dependents. But that's limited to $6000 of expenditures (for 2 or more dependents) and has the same drawbacks as above.
