For decades, I remember the Society, publications, and Elders saying that once the Great Tribulation begins, it is too late to repent or be saved. They said the "Door of the Ark will have been closed."
Now, however, look at the brand-new Clarified Understanding / New Light on this from JW.org, below.
They are still saying that the majority of worldly people will not be saved, but they are now saying it is possible.
The Simplified July Study Watchtower says this:
http://www.jw.org/en/publications/magazines/ws20150715/rapture-anointed-great-tribulation/
In a similar way in the future, when the attack against Babylon the Great is “cut short,” we cannot expect that many people will suddenly convert to true Christianity.
The non-Simplified July Study Watchtower says this:
http://www.jw.org/en/publications/magazines/w20150715/rapture-anointed-great-tribulation/
Should we conclude, though, that the destruction of the religions of Babylon the Great results in the death of all the former members of those religions? Apparently not. The prophet Zechariah was inspired to write about that time. Speaking of someone who was previously part of false religion, the account states: “He will say, ‘I am no prophet. I am a man cultivating the soil, because a man bought me when I was young.’ And if someone asks him, ‘What are these wounds between your shoulders?’ he will answer, ‘Wounds I received in the house of my friends.’” (Zech. 13:4-6) So, apparently, even some of the clergy will abandon their religious course and deny that they were ever part of those false religions.
[...] What will happen after the destruction of false religious organizations? It will be a time to reveal what is really in our heart. The majority of mankind will seek refuge in human organizations that are likened to “the rocks of the mountains.” (Rev. 6:15-17) Figuratively speaking, however, God’s people will flee to the refuge that Jehovah provides. In the first century, the interval was not a time for a mass conversion of Jews to Christianity. It was a time for action and obedience on the part of those who were already Christians. Similarly, we cannot expect that the future interruption in the great tribulation will result in an influx of new believers. Rather, it will be an opportunity for all true believers to prove their love for Jehovah and give their support to Christ’s brothers.
[...] Although we do not fully understand all that will happen during that time of test, we can expect that it will involve some measure of sacrifice.
