You are correct. Children being held to the debts of their parents is not a Western way of thought. Although, it is a Christian belief that children should be responsible for their parents, in our secular society, it is not a practice ... and should stay that way.
I went off on a tangent about the "lookback" period and Medicaid "planning" ..... In a way, hijacking your thread. Apologize for doing so.
By the way, many of us hold no debt ... with the grave exception of government "debt", with special emphasis placed upon local government. Seriously, Twelve Large a Year property tax bills on a property that rents for 1200 per month? That's the worst kind of "debt" ..... government mandated debt.