Milarepa, the early Tibetan saint/yogi said, "In horror of death I took to the mountains, and meditated on the uncertainty and the hour of death. Now capturing the fortress of deathless, unending nature of mind, all fear of death is done and over with." When we do not have the understanding of the deeper nature of mind, then of course there is fear. In fact the fear comes ultimately from ignorance. And the greatest way to remove the ignorance is by realizing the nature of mind. When one realizes the true nature of mind, it is known to be beyond birth and death. This is as I have heard of it, called "Blue Sky Mind"
This is the mind that one realizes in meditation. When you come out of the meditation, this mind can stay with you. In fact is always there, just that we sometimes lose awareness of it.