I am asking this question on behalf of someone who does not want to create a stackexchange account.
Suppose one author on a multi-author textbook that is used regularly in college courses has passed away (on the order of many months ago) but author royalty checks are still at the same amount as before, so the publisher apparently does not yet know that one of the authors is no longer alive.
Here is the main question: what is a proper way for a still surviving co-author to point out to the publisher that one of the co-authors has died without making it come off like a living co-author is just looking to increase the percentage cut of the royalties? (The living co-author suspects the royalty structure should change, but doesn't want to be so crass as to emphasize this point in the message.) You may assume there is nothing in the contract saying that in the event of a death, royalties should be sent to the one of the deceased co-author's relatives. Does the publisher usually just pay the living authors as much as before or draw up a new contract to pay out the same amount of royalties in a new way?
I suppose that if the author of a single-author textbook dies and no provision was made for royalties to continue to be sent to a next of kin, then the publisher quietly cancels the royalty contract with the original author and either (1) keeps all income for itself or (2) makes a contract with a new author to create a new edition at some point. For those in mathematics, like me, an example of the first case is probably what happened with Springer-Verlag after Serge Lang passed away while an example of the second case is Cengage after James Stewart (author of the famous calculus books) died.