If the mind is an individual's desires, fears and priorities that cause his behavior as his proactions and reactions, then psychology would be the study of the mind and how it causes – motivates – (1) his behavior as his proactions and reactions, (2) his feelings as his reactions to his actual, imagined or remembered realizations of his desires and fears,(3) his personality as his consistent proaction's and reactions in similar situations, (4) his mental problems as his unachievable and inappropriate desires, and (5) his mental solutions to his mental problems as his achievable and appropriate desires and asks/answers the ancient philosophical question ...

Q1: Why do we do what we do? [Includes thinking.]
A1: We do what we do because we have desires to do what we do, fears of not doing what we do, and priorities among our desires and fears.

Q2: What are our desires?
A2: We have physiological (unlearned) and psychological (learned) personal proactive desires for (1) survival, (2) water, (3) food, (4) shelter, (5) companionship, (6), sex, and (7) reproduction and organizational goals (desires) for purpose, structure, and functionality inre businesses, governments, and non-profit organizations.

An individual's personality is his consistent proactions and reactions in similar situations caused by his desires, fears and priorities that comprise his mind.

Studies of individuals whose personalities had been well-organized and well-liked but who suffered accidents or illnesses that altered their brains often found their personalities change to become disorganized and disliked.

This set of facts suggests that whatever is an individual's self and whatever is an individual's ego that either cause or otherwise reveal an individual's personality are brain functions which can change when the brain is altered and will be dead when the brain is dead and no longer functioning.

Thus, to address the OP, whatever is an individual's ego relevant to his personality will die when the individual's brain is dead and no longer functioning.