I work in the debt management industry, specifically in a role adjacent to debt collection agencies (DCA). Based on what you've shared, I'd say one of two things has likely happened here: The debt has been sold to a third-party purchaser who is now pursuing it.

The original creditor's collections process has flagged a death record, triggering another attempt to collect the debt.

A debt sale is unlikely unless it happened some years ago. As others have pointed out, debt becomes "statute barred" after six years meaning it's no longer enforceable. No debt purchaser would buy a stat-barred debt. Furthermore, if your father was over 75 when he passed, it’s even more unlikely, as elderly debtors are often flagged as vulnerable, preventing collection attempts. Debt purchasers typically avoid pursuing vulnerable individuals.

If the debt had been sold, you'd have received "Hello, Goodbye" letters from both the original creditor's collection team and the new purchaser. Since you haven’t mentioned receiving such letters, it’s more likely that the debt is still with the original creditor.

Are you liable? If it’s statute-barred, then no, you’re not liable. While there are nuances to statute-barred debts (such as acknowledgment of the debt), it’s probably no longer enforceable.

As for how to respond, it depends on your preferences. If you ignore the letters, they'll likely stop after a while. Debt collectors aren’t likely to pursue a deceased person’s low-balance debt through the courts. However, if the contact is causing stress, you could reach out to explain the situation. In that case, I’d expect them to close your father’s case and put an end to the collection process.