Unsent can choose whether or not they age. And yes, the reason why some do not become feinds, like Auron, Yunalesca, Seymour and Mika, is because they have strong ties to Spira, keeping them alive, so to speak.

If you go to the temples (before you fight Sin) and talk to the fayth, they give a lot of answers about Spira, the fayth, unsent and Dreams.