In the United States and most countries I'm aware of debts cannot be inherited.
If your dead aunt had a Mercedes 190SL, but also owes $200,000, you can either take both or nothing.
But yeah – they won't end up in debt themselves, unless they choose to.
It only really becomes an issue if you have a strong personal attachment to assets that have high monetary value, like e.g. perhaps your childhood home - otherwise it boils down to a financial consideration.