My uncle passed away a few years ago, and owed quite a bit of money, I believe he owed on the house and perhaps on a loan. He did not leave any money in his will, and we ended up paying for his burial. Somehow the collection agencies got my mom's address and are sending her all sorts of bills. Obviously we are not responsible for the money he owed, but how do we get them to stop sending them? It's stressing her out.
In the US, when a person has unpaid debts and dies, those debts are to be paid from any assets of the estate (as in, any assets). The executor has the responsibility to use those assets to pay the debts. Presumably the executor did that, and there are no co-signed accounts or anything like that, so your mother isn't responsible for these debts in some obscure way. The Fair Debt Collection Practices Act has a provision that you can tell a collection agency to stop communicating with you, and they must then stop communicating with you except to say they are stopping attempts to collect, to indicate possible remedies (i.e. lawsuits), or notify of an actual remedy (they have actually filed suit). Since they are no longer allowed to discuss anything with you once you give them the go-away notice, one should probably hire an attorney to exercise the nuclear option. You can also request proof that you owe the money: they are suppose to notify you of the right to dispute the debt with 5 days of first contact, which gives you 30 days to dispute the debt. Persuading a debt collector that they are pursuing the wrong person is probably easier than persuading a jury in a lawsuit.