I'm new here, but I've been playing for several years so here is my take on your question.
I'm not sure if you'll find something that spells it out directly..I think after so many generations of RPGs it's usually accepted that most effects end on death. However, here you have an item that is causing the issue and not a direct spell per say.
With these rare instances I think there are 2 questions that could help determine the status of said magic item. I think the answers to these will almost always determine that the same "rule" applies. But there are so many magic items out there that you never know...
Q1: Does the item in question work even when not worn or held..as in when they very first found the item laying in a secret chest somewhere, were it's powers active? (usually the answer will be no, but rare circumstances could change that)
A1: If the answer to that is Yes, then maybe, it depends on your answer to Q2. If the answer to that is no, then the spell/effect should end for the same reason as the answer to my Q2
Q2: What or whom does the spell effect. (Answer is usually a "creature")
What is a person? A: A "creature"
What is a dead person (non-animated/undead)?
A2: A "corpse," which is effectively an object. If the target of the spell/item is creature, then a corpse (again, non-undead) no longer fits that description and the spell/effect should end.
I think these 2 questions will help resolve those questions in these rare instances. Ofcourse, there's always the answer that it's the DMs world and they have final say, but personally, I like consistency..it ensures balance and lets the players know/understand the world their in.
Edit: A dead creature cannot make saves..they auto fail