That which is born dies. That which is not born cannot die. We do not think clearly in this matter. Some of us think that what is born may live 'forever', but that is a concept dependent on the time-illusion. Our difficulty arises in conceiving anything that is not born.
We tend to conceive everything as subject to our notion of time. But 'living for ever', i.e. going on living, is not the same thing as being eternal. The former is impossible, a pure illusion; the latter the only reality. Being eternal is never having been subject to the conception of time.
Being eternal is not 'going on living': it involves no process of becoming: being eternal consists simply in Being.