Can a relative be compensated from the state or Government for caregiving to a parent?

I know it sounds cold to want to be compensated for taking care of your parent or parents, but the bills still have to be paid and when your losing time at work behind them needing you ,something has to be done to make up for the loss of income.If Medicaid is going to pay somebody to help out then why can't they just pay the relative that's already taking care of the parent or parents.I'm sure the parents would prefer to have their family do it anyway