There is no doubt that there will be a great harvest of souls after the Rapture (Rev. 7:9-14). Some will be convicted by the Rapture itself. Others will be converted by the preaching of either the Two Witnesses in Jerusalem (Rev. 11) or the 144,000 Jewish disciples who will proclaim the Gospel (Rev. 7). Some will repent in response to the judgments of God (Isa. 26:9). Others will respond to an angel of God who will preach the "eternal gospel" to all the world at the end of the Tribulation, right before the final pouring out of God's wrath (Rev. 14:6).
The controversial issue is whether or not those who have heard the Gospel before the Rapture and have rejected it will be allowed to respond and be saved after the Rapture. Some take the position that such people will be able to accept Jesus as Lord and Savior after the Rapture. I hope they are right about this. But, not all prophecy teachers would agree. The reason for the controversy is a passage in 2 Thessalonians 2:8-12 which seems to indicate that such people will continue to reject the Gospel after the Rapture. Here's the passage. Read it for yourself and draw your own conclusion:
"And then that lawless one will be revealed whom the Lord will slay with the breath of His mouth and bring to an end by the appearance of His coming; that is, the one whose coming is in accord with the activity of Satan, with all power and signs and false wonders, and with all the deception of wickedness for those who perish, because they did not receive the love of the truth so as to be saved. For this reason God will send upon them a deluding influence so that they will believe what is false, in order that they all may be judged who did not believe the truth, but took pleasure in wickedness."
This passage seems to teach that people who have rejected the truth before the Rapture will continue to do so. Because of this passage, I cannot say with absolute confidence that those who have rejected the Gospel before the Rapture will have the possibility of accepting it afterwards. I hope they are right, but I would not want to give such people any false hope.