Paul says otherwise:
Philippians 1:20 (NASB) according to my earnest expectation and hope, that I will not be put to shame in anything, but that with all boldness, Christ will even now, as always, be exalted in my body, whether by life or by death.
Because Christ is eternal, Paul is eternal.
Because Paul is eternal he will not be put to shame even by his death.
If Paul were not eternal, he would not be exhalting Christ always.
15 Some indeed preach Christ even from envy and strife, and some also from goodwill: 16 The former preach Christ from selfish ambition, not sincerely, supposing to add affliction to my chains; 17 but the latter out of love, knowing that I am appointed for the defense of the gospel. 18 What then? Only
that in every way, whether in pretense or in truth, Christ is preached; and in this I rejoice, yes, and will rejoice.
19 For I know that this will turn out for my deliverance through your prayer and the supply of the Spirit of Jesus Christ, 20 according to my earnest expectation and hope that in nothing I shall be ashamed, but with all boldness, as always, so now also Christ will be magnified in my body, whether by life or by death. 21 For to me, to live
is Christ, and to die
is gain. 22 But if
I live on in the flesh, this
will mean fruit from
my labor; yet what I shall choose I cannot tell. 23 For I am hard-pressed between the two, having a desire to depart and be with Christ,
which is far better. Philippians 1:15-23
Paul will not be put to shame by those who preach Christ from envy and strife, by those who preach from selfish ambition, supposing to add affliction to his imprisonment.
... "as always", is a reference to how Paul was both living his life, and had lived his life to glorify Christ.
These verse's have nothing to do with Paul "being eternal", nor being put to shame by his death.
Whether Paul lives or dies, his life was spent exalting and glorifying Christ.
JLB