The change it speaks of is the change from the mortal, fleshly body to the spiritual body at out bodily death (1 Cor. 15:44).
When we have trouble harmonizing the scriptures, we should immediately recognize that our understanding is at fault. If we let the Bible speak, and pay attention to what it says, rather than to what men have twisted it to mean, then the perceived "problems" with the scriptures disappear. Everything in the scriptures harmonize when we can drop the dogma of church teaching.
1 Cor. 15:52 speaks of the raising of the dead. False teachers were troubling the church at Corinth saying that there was no resurrection. The Corinthians were concerned about their loved ones who had died before Christ's return, and Paul was addressing that issue.
I Cor. 15:31-32,
"Every day do I die, by the glorying of you that I have in Christ Jesus our Lord:
32 if after the manner of a man with wild beasts I fought in Ephesus, what the advantage to me if the dead do not rise? let us eat and drink, for to-morrow we die!" (YLT)
1 Cor. 15:35-36,
" But some one will say, `How do the dead rise?
36 unwise! thou -- what thou dost sow is not quickened except it may die;" (YLT)
Confusion reigns when we do not stay on topic. Their concern was what happens after the body dies, and the discussion is the "rising again" after death.
No where in this chapter is there any concept or discussion of a "rapture", or of anyone being lifted into the skies before death of the body. The scriptures do not support any of the current teaching of a rapture.
Everyone dies. We are born, we live the time we have, and then the body dies as vs. 50 confirms:
"And this I say, brethren, that flesh and blood the reign of God is not able to inherit, nor doth the corruption inherit the incorruption;" (YLT)
Flesh and blood - the body - does not inherit the promise of eternal life in heaven. The corruptible flesh decays, the body dies. For those who die in the Lord (Rev. 14:13), it is raised after death incorruptible.
So, Paul concludes in vs. 51-52 the manner of the change after death. The rising again - the raising of the dead - takes place in a twinkling of an eye. In a moment, in a snap of the fingers we inherit the form of the spiritual body raised in glory (vs. 44).
Resurrection can only happen after we die. Then, the question comes to the timing that keeps being twisted in vs. 52. Many take the first half of the verse "the last trumpet" and make it simultaneous with the last half "we shall be changed" for everyone.
Since our resurrection - rising again of the dead - can only happen after we die, then the "we" of vs. 52 is speaking of our change after we die. There are 3 parts to the resurrection, and most people are confused about it.
Part I - Christ, the first fruits from the dead (1 Cor. 15:20) approx. AD. 31-33; then
Part II - the group resurrection of all those who had already died and were sleeping in Hades (Matt. 25:31-46) at His coming in A.D. 70 when He separated the sheep (His saved) from the goats (the rebellious lost); and
Part III - the change to the on-going, individual resurrection that is now in process, and has been ever since His second appearance to that generation of the first century A.D.
We have to get rid of the blinders that have been placed over our eyes so that we can see what the Bible really says about His coming. His second appearance was promised to that generation in which He was made manifest on earth. It was always promised to the first century AD who saw His death on the cross, who saw His resurrection, and who saw His ascension into heaven.
Heb. 9:28 was a promise to them - those first century Christians - that they would see Him a second time. You cannot have a second appearance of Him if you have never seen Him a first time. So, no other generation could have a second appearance of Him other than that first century AD generation who received the promise.
We are not looking for a future "end of the world" coming of the Lord. He reigns at the right hand of the Father now. He will come in judgment against nations any time He needs to just as He demonstrated throughout all of the OT. But, He has promised that never again would He destroy all living things as He had once done (Gen. 8:21).
The rainbow pictured around the throne scene in Rev. 4:3 was a reminder of that promise. The judgment prophesied upon those wicked Jews was not going to be a world-wide destruction.
His second coming was to punish that wicked generation of vipers, the one He told would pay for all the righteous blood shed from all generations past, from Abel to Zacharias (Matt. 23:35). He did not delay in that judgment, and it was poured out upon those who pierced Him (Rev. 1:7) and those who persecuted His saints in A.D. 70 at the destruction of Jerusalem and that Mosaic sacrificial temple.
So, Paul was telling the Corinthians that the dead in Christ would be raised at His soon to happen coming, in their generation. Christ did raise them from Hades. He took all the saved (sheep) home with Him. And, then He cast the lost into the lake of fire. And, then He threw Hades into the lake of fire (Rev. 20:14). See the sequence of events outlined in Matt. 22:1-14 for the destruction of Jerusalem and the judgment that immediately followed.
Since Hades is gone, and has been gone for almost 2,000 years, the raising of the dead has been happening on a continual basis for every one as they die. The saved are taken home to heaven; and the lost are judged and cast out to outer darkness (Matt. 22:13).
See my post "The Resurrection in Three Parts" at my blog ShreddingTheVeil. See the other posts Parts I - X of "It's Not The End of The World" for the proof from the scriptures of His return in the first century A.D. You might also explore the other articles there for the series on The Signs of Revelation, The Beast of Revelation, The Whore of Babylon, etc.