Can a sibling get paid to take care of a parent with dementia?

If the family agrees, there could be arrangements made to pay an adult child for the care. It should be something on paper, probably witnessed by someone outside of the family. An estate attorney is a good idea (or an elder law attorney). It's often more cost effective to pay a family member an agreed amount if the parent and siblings all come to terms with it, than to hire an agency, but that only works if the whole family is together on it and the person is responsible. As to government help - that's a different issue. If the person is on Medicaid, you'd have to check with the Medicaid people.
Carol