One way to handle this is in one’s will. One dollar will do it.
Perhaps some lawyer out there will settle this for us, but I have been told that that is not necessary. One can just as easily state that you haven't forgotten about him/her/them, you just choose to not leave them anything.
Now, this may not apply to siblings, cousins, etc. and may apply to children (of which I have none so the issue never came up).