It chops and changes all over the world, but generally speaking (in western countries at least) the debt does not pass on.
This article provides a calm rundown of the situation in the USA. Do note the section about "generally no, but maybe" if a large asset transfer occurred just before death. Also, it's worth noting that most states have tweaks to the laws - for example, the state of Florida makes sure that medical bills get full freight while credit card companies take a back seat.
In the UK, they take the rather humane approach that funerary debts be paid first, then the creditors can have at it. Insolvent deceased estates in the UK are administered according to normal bankruptcy laws. To see a full list of the many descriptive resources available from HMRC, see this search, but also see this article for a more general overview.
In Canada it will be defined in law by each province, but run along lines similar to the US and UK. As an example, see this doc from the Saskatchewan gov discussing the order in which debts will be paid, especially page 5. And no, estate administrators are not responsible for the debts.