Perhaps when we hear about "the time of the dead," we think of those who have already physically died. But that's not necessarily the case when it comes to the language of the Bible. In the Bible, God reckons sinners to be dead (spiritually) in trespasses and sins, even while they still live physically:
Ephesians 2:1 And you hath he quickened, who were dead in trespasses and sins;
1 Timothy 5:6 But she that liveth in pleasure is dead while she liveth.
Therefore, when God speaks of a time wherein He will judge the "dead," this very well could mean the spiritually dead as well as those who have physically died. Once we realize this, then verses that refer to God's judgment upon the "quick and the dead" begin to open up to our understanding:
2 Timothy 4:1 I charge thee therefore before God, and the Lord Jesus Christ, who shall judge the quick and the dead at his appearing and his kingdom;
The Old English word "quick" means to “live” or to be “alive.” Since we now know that God is judging the just (elect) and the unjust (non elect) in this prolonged time of spiritual judgment, we can clearly see that the reference to the "quick" is a reference to those that Christ has saved; while the reference to the "dead" is describing all unsaved people whether they happen to be presently physically alive or not.