In general I think if a DT member dies, his trust is still valid and I don't see a reason why it should be deleted. The only exceptions to this are cases where someone might have successfully appealed the neg. For example, if I suddenly died and one of the members I'd tagged for account selling had somehow turned into an extremely trusted member, then my feedback should be removed. That's the kind of case which would have resulted in a successful appeal for me to remove it.
Your trust ratings are based on
your judgement of what is deserving of a tag. Your judgment is subject to change over time as you gain additional insight and experience. You may leave a rating today that you would disagree with in the future. There is no universal criterion for what deserves a rating (this is part of a larger problem with the trust system, but that is another discussion).
The question ultimately is who gets to decide if someones appeal to have a rating removed is successful? If you are around, then the answer is you, and this is based on your judgment. If you are not here because you passed away, are retired from the forum, or otherwise, then the decision becomes complicated. If someone else, or a group of people gets to decide then those who have you on their trust lists may not trust the judgment of this group of people. If you are alive but are (temporarily) away from the forum, perhaps unexpectedly, you might not agree with the decision of whoever decides the appeal, and if the rating is removed and you disagree then adding it back on would be controversial.
My suggestion would be to treat this as if someone will not remove a particular rating. If this means you take any particular action, or dont take any particular actions, I would do the same in this case.