I have no idea about the teachings of one John Nelson Darby. However, it is bible teaching that when the Lord does come at his second coming that many will be caught up into the clouds to meet him and those left behind will suffer the wrath of God and be burned as stubble.
Matthew 24:39-42
39 And knew not until the flood came, and took them all away; so shall also the coming of the Son of man be.
40 Then shall two be in the field; the one shall be taken, and the other left.
41 Two women shall be grinding at the mill; the one shall be taken, and the other left.
42 Watch therefore: for ye know not what hour your Lord doth come.
1 Thessalonians 4:16-17
16 For the Lord himself shall descend from heaven with a shout, with the voice of the archangel, and with the trump of God: and the dead in Christ shall rise first:
17 Then we which are alive and remain shall be caught up together with them in the clouds, to meet the Lord in the air: and so shall we ever be with the Lord.
Doctrine and Covenants 109:74-75
74 And be adorned as a bride for that day when thou shalt unveil the heavens, and cause the mountains to flow down at thy presence, and the valleys to be exalted, the rough places made smooth; that thy glory may fill the earth;
75 That when the trump shall sound for the dead, we shall be caught up in the cloud to meet thee, that we may ever be with the Lord;
Doctrine and Covenants 88:96
96 And the saints that are upon the earth, who are alive, shall be quickened and be caught up to meet him.
Malachi 4:1-6
1 For, behold, the day cometh, that shall burn as an oven; and all the proud, yea, and all that do wickedly, shall be stubble: and the day that cometh shall burn them up, saith the Lord of hosts, that it shall leave them neither root nor branch.
2 But unto you that fear my name shall the Sun of righteousness arise with healing in his wings; and ye shall go forth, and grow up as calves of the stall.
3 And ye shall tread down the wicked; for they shall be ashes under the soles of your feet in the day that I shall do this, saith the Lord of hosts.
4 Remember ye the law of Moses my servant, which I commanded unto him in Horeb for all Israel, with the statutes and judgments.
5 Behold, I will send you Elijah the prophet before the coming of the great and dreadful day of the Lord:
6 And he shall turn the heart of the fathers to the children, and the heart of the children to their fathers, lest I come and smite the earth with a curse.
When Jesus appears at his second coming, the dead in Christ will rise to meet him and those who are alive on the earth who are not numbered among the wicked will also be caught up in the clouds to meet him. The wicked who remain on the earth will be burned as stubble. This is what the Bible and other revelations have testified to regarding Jesus' second coming.
You're quoting from the book Joseph Smith wrote.
Read the Revelation letter to the 7 churches. Read the Bible.
This generation" doesn't mean "now"—it means the generation of the disciples who sat and listened to Jesus’ answer to their questions about:
When will these things happen?
What will be the sign that they are about to be fulfilled?
These questions follow Jesus’ prophetic statement that “not one stone [of the Temple] will be left unturned.” If those are the questions to be answered in the whole of Mark 13, then what ramifications for interpretation does the text leave us with?
After the questions, the chapter continues by answering with the kind of things that will take place leading up to the destruction of the Temple:
false messiahs (several were present in the first century)
wars (the Jewish War of 66-70 AD)
food shortages (imagine Jerusalem were surrounded, where would food come from?)
earthquakes (happened)
persecution (by the Jews and Rome)
the need to flee to the mountains (smart thing to do if your city is going to be burned to the ground soon, don’t you think?!)
the gospel being preached throughout the nations (Paul’s missionary journeys, etc.).
Then, there will be cosmic signs (sun darkened, moon dimmed, stars falling, earthquakes), which is a Jewish way to describe cataclysmic political disaster and change.
There are several examples of this language in the Old Testament that always point to a political reality, not the literal convulsion of the cosmos.