I went through this when my father-in-law passed back in 2012. For "about" a year after his passing, I was getting bills (mailed to his address in his name and forwarded to me) in the mail from creditors and debt collectors. I simply attached a statement stating he passed and all of his estate had been exhausted to meet outstanding debts. Then included a copy of the death certificate. Mailed it back, and never heard from that creditor or credit collector again.
On a somewhat humorous side, he received a notice for jury duty in 2014. When he didn't show a sheriff's deputy showed up at my house looking for him. (My house was his last residence before he passed.) Told the deputy he no longer lived here, and he cut me off before I could finish my sentence by saying "because he passed in 2012", and was politely "demanding" to know where he was. Told the deputy I didn't know the specific address, but would be happy to take him there if he wanted to follow me in my truck.
We arrived at the gravestone and my final response to the deputy before leaving him standing there speechless and looking like an idiot was "I home you bought a shovel."
