Bureaucrap. The most advanced product of Socialism. (Totalitarianism)
Nobody understands the rules, so they can make them up as they go along.
In some states, it’s not just the estate of the deceased that is liable for Medicaid repayment. The children are personally liable and the children’s assests can be seized to repay the State. This is regardless of whether or not the children had any say-so about the parent going onto Medicaid. Children may not have even known the parent(s) were on Medicaid, but that doesn’t matter.
My advice, if you have parents who are senior citizens, check your state law and get thee to an attorney who specializes in Estate Planning.