Has God never approached anyone “on the way out” with a final and best offer... I cannot say that, I do not have a scriptural basis for it. It is up to each soul to refuse or accept God qua Savior (which is actually another way of saying the name of Jesus — in Aramaic this is Yeshua, or the Savior).
Statements like yours, lacking a context, only appear to depict a cruel and capricious God, rather than a God that respects our choices deeply enough to let us damn ourselves rather than having a puppet salvation shoved down our throat.
I wonder why billions of Asians who have already lived and died over the centuries chose to burn forever. That is the fate in store for the vast, vast majority of them who were non-Christian, according to Scripture.
Why do you think they made such a choice?
The latter part of Luke 16 seem to give the best view of dying, both for the faithful and unfaithful, and we cannot expect someone “...from the dead...” to teach us more perfectly...Jesus died, came back from the dead and is our teacher today (Hebrews 1:1-2).