The passage from the Book of Malachi contain a stark and threatening picture of the end of time and final judgment:
See, the day is coming, burning like an oven, when all the arrogant and all evildoers will be stubble; the day that comes shall burn them up so that it will leave them neither root nor branch.The reading from Luke recounts the words of Jesus about the end times: wars, insurrections, earthquakes, famines, plagues, etc.
We face these realities in our own life. As we contemplate our individual death, we understand more fully the meaning of annihilation; we face the complete destruction of who we are, or at least it seems like that. At the end of the passage from Luke, Jesus gives us a clue about what our faithful stance should be: "By your endurance you will gain your souls."
In other words, as disciples of Christ, we are to live our lives, not in light of what will happen at the end, either of our lives or the end of all existence. Rather we are to live out the reality of who we are as believers: sons and daughters of a loving God. Our lives are to express that reality rather than express our fear of what might happen at our death if we don't.