Can people repent and be saved after the rapture?
Yes. Millions will repent and come to Christ for salvation during the time following the Rapture of the church.
We know this because John, who was given a vision of that time saw millions of people wearing dazzlingly white robes standing before the throne of God. There were so many that they couldn"t be counted by a man. An "elder" in heaven asked John who these people were. John didn't know, but knew that the one asking did know. The conversation went like this, according to John, who recorded it in Revelation 7.14:
"And I said unto him, Sir, thou knowest. And he said to me, these are they which came out of great tribulation, and have washed their robes, and made them white in the blood of the Lamb."
So, obviously, people can repent and be saved after the Rapture occurs. However, the issue becomes somewhat more problematic when we ask whether those who during this present era, the Church Age, have heard the gospel, understood that Jesus is the only way to salvation, yet refused God's grace gift for redemption, will have another chance during the Tribulation. God Himself will send those people who have hardened their hearts and rejected His Son a "strong delusion." Scripture says:
"And for this cause God shall send them strong delusion, that they should believe a lie: That they all might be damned who believed not the truth, but had pleasure in unrighteousness" (2 Thessalonians 2.11-12).
Many believe the previous verse means people who had a chance to be saved before the Rapture but rejected Christ won't have any hope of salvation after the Rapture. But the 2 Thessalonians 2 account doesn't actually say that will be the case. This Scripture indicates that all who reject God's call to salvation and choose to stay in their sin will be given over to Satan and his man of the Tribulation hour, Antichrist. They will fall for his lies and be damned forever. They will be damned without hope of redemption when they take Antichrist's mark. (See Revelation chapter 13.)
Antichrist's lies will be powerful and alluring, much like Lucifer's lies were almost irresistible to Adam and Eve in the Garden of Eden. One's chances for coming to a belief in Jesus Christ for salvation will be greatly hindered during the Tribulation. Today is the day of salvation!