Funny I had a discussion about this just recently, I asked them do you think every saved soul will be taken at the rapture . They immediately answered " why yes , of course " .
I replied to them , " Well then who will be left to witness to those left behind in the final days " ?
All I got was a deer in the headlights !
There will be plenty who have ignored any warning about accepting Christ before it's too late. Those folks, obviously, will be left behind.
For some of them that heard the Gospel, the light will then come on. They will then realize that they should have accepted Christ but will do so after they have seen the rapture. Some theologians disagree with this theory as the Holy Spirit will be taken out of this world. I don't think He will be taken out but His restraining power will be removed.
I think that it may still be possible for someone to accept Christ after the rapture and thereby receive the Holy Spirit. Nevertheless, they are going to experience hell on earth as nobody has ever experienced it before.
Don't forget about the two witnesses mentioned in Revelations Chapter 11 and the 144,000 evangelists of Chapters 7 and 14.
One last note about people not accepting Christ but being left behind after the rapture. Some people are under the mistaken idea that they can wait till after the rapture, then accept Christ.
That might be okay accept for a couple of problems:
1) They don't know if they will still be living up to and after the rapture. In other words, one doesn't know when or how they are going to die. They could assume room temperature before the rapture then they will be in hell for all of eternity.
2) If the theologians, that disagree with the aforementioned theory, are correct then there is the possibility that one's heart could be so completely hardened that he or she will never recognize Christ as their savior after the rapture.