Will There Be Christians Saved After the Rapture?

A question I'm asked quite often is "Will there be Christians after the rapture?" If the Holy Spirit is taken away from the earth, how will He draw men to salvation?

Lars Justinen, "Robe of Righteousness"

These are good questions and I'll do my best to offer scriptural answers.
The first basis to answer this is to understand that God has plans. I think we all agree on that. Jeremiah 29:11 reveals that God has plans for Israel. Isaiah 14:26 reveals that God uses nations to fulfill His plans. Amos 3:7 reveals that God has plans and that He reveals them to His prophets (and in the NT, through the Holy Spirit Who set them down in the bible).

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In addition, God's plans are different for His people & His nation Israel; and the church who is His bride. This is called dispensational biblical interpretation. You can read about this doctrine here in succinct fashion-
"What is dispensationalism and is it biblical?"
and here
"What are the seven dispensations?"
All it means is that God has different plans for Israel and the Bride. Ultimately however, His plans merge n general by His grande redemptive plan. No matter what dispensational epoch we lived in, we will all be trophies of His grace for all eternity. And how we all get there is the same (Old Testament believers from Adam, to Noah, to Moses to Abraham to Anna- through belief in and faith of the promise of a coming savior; for New Testament believers, from John and Peter, Mary, Paul, and on through to today's born again believers through the world, belief in and faith of the promise of an already risen savior).
Secondly you have to understand that the rapture will occur prior to what the Jews call the Time of Jacob's Trouble (Jeremiah 30:7) and known to New Testament believers via the Olivet Discourse Matthew 24 as the Tribulation and Great Tribulation. I am not going to argue this fact, it is explicitly and implicitly set out in scripture that this is so. I have written about it at least ten times on this blog. Search in the search box above for 'pre-trib' and many results will come up.
Once you understand that the Age of Grace in this dispensation will end with the rapture and then the tribulation begins, we also can go on with answering the post's main question. Will there be Christians after the rapture?
Yes. There will be Christians after the rapture.
Biblical proof of this is myriad. For example, Revelation 4:1 seems to be the pivot point in the Book's largely chronological unfolding of events. The first three chapters are letters to actual churches of John's day outlining praise and/or condemnation of their deeds. This section of Revelation is also a metaphor for believers in days of yore and us today in church, as to what Jesus will praise or condemn in our corporate worship life. As we begin Revelation 4:1 we read from then on, 'These are things which will take place after'. By Revelation 5, the seals are about to be opened and we are told, gloriously, 
“Weep no more; behold, the Lion of the tribe of Judah, the Root of David, has conquered, so that he can open the scroll and its seven seals.” (Revelation 5:5)
In Revelation 6, when He opened the fifth seal unleashing the wrath of God, we read:

"I saw under the altar the souls of those who had been slain for the word of God and for the witness they had borne. They cried out with a loud voice, “O Sovereign Lord, holy and true, how long before you will judge and avenge our blood on those who dwell on the earth?” Then they were each given a white robe and told to rest a little longer, until the number of their fellow servants and their brothers should be complete, who were to be killed as they themselves had been."

Those who were slain for God and their witness are Christians. They are not Christians from the Age of Grace because the Christians were raptured before the beginning of the Tribulation. These are souls who had come to saving knowledge of Jesus as Savior afterwards. How do I know this? Because all Christians were raptured prior to the wrath. The Bride is not appointed to wrath. (1 Thessalonians 5:9). The wrath begins in Revelation 6:1.
Another question that is asked is, how did they become Christians after the rapture if the Restrainer had been removed? This question is in reference to 2 Thessalonians 2:6. The Restrainer mentioned here is the Holy Spirit. One of His ministries is to restrain the devil in raising up the man of sin before his time.
MacArthur explains,

So he says to the Thessalonians...you know this, you know that there is a force, a supernatural force that keeps Satan from doing what he would otherwise want to do. Listen, you think the world is bad now, you haven't seen anything yet. Fortunately if you know Christ you won't see it, but in the day of the Lord when the restrainer is gone and all hell breaks loose, the world will see what happens when God does not restrain Satan in his plans.

In Genesis chapter 6 there is an important verse, verse 3, "Then the Lord said, My Spirit shall not strive with man forever." What you have here is a concept. The Holy Spirit battling against wicked men. And God says My Spirit isn't going to do that forever. My Spirit isn't going to fight your wickedness forever. It wasn't long until He drown them all, right? And I think you have there the work of the Holy Spirit that is a restraining work. The Holy Spirit was battling against the flood of wickedness in the ancient world. In Acts chapter 7, one other verse that shows us the Spirit's ministry in this kind of area. In Acts 7:51, "You men who are stiff necked and uncircumcised in heart and ears are always resisting the Holy Spirit." Now here again [in 2 Thessalonians 2:6] you have the Holy Spirit battling against sin, battling against iniquity, battling against evil, trying to restrain, as John tells us, to convict in John 16. (more here)

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So the Christians who are part of the Bride are whisked away before the wrath begins. Christians who come to faith after wards are not part of the Bride though they are appointed to eternity as well. The man of Sin is unveiled and the total saturating sin as it was in the Days of Noah repeat, (Dan 9:24) except worse. Yet Christians still come to saving faith. That is because though the restrainer is not holding back sin nor the man of sin any more he is still drawing men.
God supernaturally seals 144,000 super evangelists (Revelation 7:1-8) and by Revelation 9, a great multitude of the redeemed are standing before the throne and praising Him!
God also sends an angel flying at mid-heaven to pronounce the Gospel (Revelation 7:6) and the result is that by Revelation 7:12 there are saints enduring in the faith.
None of this would be possible if the Spirit had not drawn them. (John 6:44, John 6:65). Even during the Tribulation the Father, the Son and the Spirit are working in perfect unity to perform His plan and to redeem trophies of grace for His glory!
Finally, of course there are Christians who come to faith after the rapture, because it is those believers who are alive - in the flesh- and left upon the earth who enter the Millennial Kingdom. GotQuestions explains,

Matthew 25:31-46 is another passage that should be considered. This passage is commonly called the separation or judgment of the sheep and the goats. The sheep and goats refer to righteous and unrighteous Gentiles. Christ will judge the unrighteous Gentiles (goats), and they will be cast into the lake of fire for eternal punishment (Matthew 25:46). Therefore, no unbelieving Gentile will survive to live on into the millennial kingdom. The righteous Gentiles, or sheep, will live on into the millennial kingdom. Read more

The Lord our God is a God of steadfastness to His persecuted ones. He sent His Son to be persecuted and die for our iniquities, and thus the finished work of His salvation to the elect was completed when God exhausted His wrath in Jesus.
The Holy Spirit continues to draw all those people whom God had written in the Lamb's Book of Life before the foundation of the world. (Revelation 13:8, 1 Peter 1:20, Matthew 25:34). No matter when a believer lived or will live, in the Garden in the Age of Innocence, the Age of Conscience which was pre-flood, the Age of Human Government which was post flood, Age of Abraham and the Promise, during the Age of Law with Moses, the Age of Grace which is the Bride, or the Millennial Age to come, if your name is in the Lamb's Book of Life you are His trophy of grace and will never be set aside, lost or otherwise disowned.
As Paul says in Romans 8:23,

"And not only the creation, but we ourselves, who have the firstfruits of the Spirit, groan inwardly as we wait eagerly for adoption as sons, the redemption of our bodies."

So yes, Christians will come to faith after the rapture, as they will also in the Millennium age after that. What a wonderful eternity we will have, sharing and listening to the stories of His graceful redemption of humans throughout the ages, all the while praising the Holy Spirit who worked throughout to draw men unto the God of Salvation! (Hosea 13:4)

Lars Justinen, "Robe of Righteousness"