Information by the US Postal Service suggests that, stopping junk mail is best accomplished by contacting the Direct Marketing Association and requesting to be put onto the "Decease Do Not Contact List."
If you get mail from a deceased person who lived with you, you can manage the mail. If you are not the executor or trustee, managing the mail means forwarding the mail to the executor so that they can deal with it. Visit the US Postal Service for more Information.
Forwarding mail of a deceased person to a new address requires filing a request at your local post office. This necessitates providing valid proof that you are the appointed executor or administrator and authorized to manage the deceased person’s mail. If the estate has no named or acting executor, it may become necessary to file probate.