I know that if you have a household in My Households, that keeps them from being culled by the game. But does it prevent Sims from aging/dying or is that only Played households?

My current household is getting unwieldy with 6 Sims and a cat. I'm thinking about moving my founders, Liam and Cali O'Dourke, to a smaller place on their own when they both reach the top of their current careers (I have two goals for them and their descendants -- to reach the top of all the careers and to complete all the collections possible) and also go ahead and age them to Elder to focus on their daughter, Selena, and her family. (They'll also take the family cat, Fiona, so Selena's boys can take the dog. If I keep them in My Households but mark them as unplayed, will they eventually die (which is what I want, Circle Of Life and all that) or will they remain immortal unless I put them in Other Households?