No, the people not taken to heaven at that time will die.
Rev. 22:11,12 He that is unjust, let him be unjust still: and he which is filthy, let him be filthy still: and he that is righteous, let him be righteous still: and he that is holy, let him be holy still.
And, behold, I come quickly; and my reward is with me, to give every man according as his work shall be.
The judgement is over. No more chance for the lost.
Matt. 24:27 For as the lightning cometh out of the east, and shineth even unto the west; so shall also the coming of the Son of man be.
It won't be a secret.
Jeremiah 25:33 And the slain of the Lord shall be at that day from one end of the earth even unto the other end of the earth: they shall not be lamented, neither gathered, nor buried; they shall be dung upon the ground.