Hebrews 2:14-15 contains an intriguing observation:
14 Since therefore the children share in flesh and blood, he himself likewise partook of the same things, that through death he might destroy the one who has the power of death, that is, the devil, 15 and deliver all those who through fear of death were subject to lifelong slavery. Hebrews 2:14–15 (ESV)
Very little appears in the commentaries concerning the fact of being subject due to the fear of death. Calvin, in his commentary on Psalm 6:5, makes the following observation adds a bit concerning the nature of the fear of death:
From this passage, we are furnished with the solution of another question, why David so greatly dreaded death, as if there had been nothing to hope for beyond this world. Learned men reckon up three causes why the fathers under the law were so much kept in bondage by the fear of death. The first is, because the grace of God, not being then made manifest by the coming of Christ, the promises, which were obscure, gave them only a slight acquaintance with the life to come. The second is, because the present life, in which God deals with us as a Father, is of itself desirable. And the third, because they were afraid lest, after their decease, some change to the worse might take place in religion. But to me these reasons do not appear to be sufficiently solid. David’s mind was not always occupied by the fear he now felt; and when he came to die, being full of days and weary of this life, he calmly yielded up his soul into the bosom of God. The second reason is equally applicable to us at the present day, as it was to the ancient fathers, inasmuch as God’s fatherly love shines forth towards us also even in this life, and with much more illustrious proofs than under the former dispensation. But, as I have just observed, I consider this complaint of David as including something different, namely, that feeling the hand of God to be against him, and knowing his hatred of sin, he is overwhelmed with fear and involved in the deepest distress. The same may also be said of Hezekiah, inasmuch as he did not simply pray for deliverance from death, but from the wrath of God, which he felt to be very awful, (Isaiah 38:3.)
John Calvin and James Anderson, Commentary on the Book of Psalms (Bellingham, WA: Logos Bible Software, 2010), Ps 6:5. Unfortunately, he does not go further and address the matter of how the fear of death leads to the slavery of sin.