Yes, in fact the details vary some depending on which state you're in and how you're related to the deceased. In general, though, I'd treat unsolicited calls at

Yes, in fact the details vary some depending on which state you're in and how you're related to the deceased. In general, though, I'd treat unsolicited calls attempting to get you, personally, to pay for a dead relative's debts, as bullshit until you're 100% sure they're not. Most (all?) state governments have FAQs for this sort of thing online, and the federal government also offers guidance (all trivially Googleable).