In the state of Ohio, if a parent dies with outstanding medical bills or other debts, can their living children be held responsible?

If a parent passes away with no assets to their name and racked up significant debt (specifically medical bills, utility bills and child support) is it possible their child/children would be responsible for paying these bills? With no assets, there would be nothing to liquidate in order to pay off the debts. I indicate state of Ohio as I understand some states may have different laws. If the answer is yes, is there any way for a father to protect his children against passing along this burden?