Jeremiah 38:2-3 ESV
“Thus says the LORD: He who stays in this city shall die by the sword, by famine, and by pestilence, but he who goes out to the Chaldeans shall live. He shall have his life as a prize of war, and live.  Thus says the LORD: This city shall surely be given into the hand of the army of the king of Babylon and be taken.”
Jeremiah's words to the people of Jerusalem was clear: Surrender to the king of Babylon and you will live. Stay in this city and you will die.
These words of course sounded like treason to the Jews:
Jeremiah 38:4 ESV
Then the officials said to the king, “Let this man be put to death, for he is weakening the hands of the soldiers who are left in this city, and the hands of all the people, by speaking such words to them. For this man is not seeking the welfare of this people, but their harm.”
These officials thought that to go outside the city to the Babylonians meant certain death. Even though God's Word promised that they would live, they chose to believe in their own thoughts, rather the promise of God.
Hence, this was the ultimate test: those who believe in God's word would go out and live. Those who disbelieve in God's word will stay, fight to the end like fools, and die, and suffer the wrath of God unleashed.
The instructions of Jeremiah is a type of the Gospel instruction given to ALL of humanity: turn your back on the world (i.e. the world system of sin, run by Satan), surrender to Jesus and live forever. Remain part of this world, resist the authority of Jesus over your life, and experience the eternal wrath of God.
There are only two options. Of course, surrendering to Jesus "sounds" like death: it is death to self, death to one's own will, one's own selfish desires and ambitions. But it is actually the way to life (indeed, it IS life itself):
Mark 8:34-35 ESV
And calling the crowd to him with his disciples, he said to them, “If anyone would come after me, let him deny himself and take up his cross and follow me.  For whoever would save his life will lose it, but whoever loses his life for my sake and the gospel's will save it.
Just as to "go out to the Chaldeans" meant life to the citizens of Jerusalem, to lose your life for Jesus and the Gospel is save it forever. That is the infallible promise of God, in Christ.
But, what does it mean to "lose your life for Jesus", practically, besides martyrdom? It means, when someone sees my life, all they see is Jesus Christ and His Gospel! When someone who doesn't know Christ sees me, they say, "this guy has NO LIFE, besides this "Jesus" and "Gospel" business!"
It means Jesus and the News of His glorious death and resurrection has so taken over and consumed all that we are, that besides those things, we are seen as nothing and having nothing. That besides Christ and the message of Him Crucified we are nothing but an empty shell! That's what it means to "lose my life for Jesus and the Gospel's".
Now, when we live in such a way, people who belong to this world system (especially churchgoers and religious people) will accuse us of a kind of 'treason'. They will say that we are being too 'extreme'. They will say that one must not empty oneself SO MUCH for Jesus and the Gospel. Jesus can just be one of the many accessories of a person's life. You can still keep your "life" and have Jesus too, they will say. Such preaching of 'Jesus + Nothing = Everything' (where ME and my ego is included in that "Nothing"!!) "weakens the hands of the people", they will say. It hurts our self-esteem! We need to FIND ourselves, not lose ourselves for the glory of Another!
But, in the midst of such devilish voices (including especially those of our own deceptive hearts), we must believe in the unshakable promise of God: to LOSE our lives, to go out to Jesus Christ and hand over our kingship to Him, is our ticket to freedom and life! To refuse to do that is to pronounce a death sentence upon ourselves.