Does the Parable of the Ten Virgins refer to the Rapture?
Matthew 24 and 25 are a unit, being a continued narrative. The discourse of the Lord flows from questions about the temple, His coming, and the end of the age. The focus on "signs of His coming" indicates the Jewish setting of the passage, for "the Jews require a sign" (1Co 1:22) and "the times and seasons" that the Lord gives here are related to the Day of the Lord and the time when sudden destruction (1Th 5:1-3) will come on those who trust a covenant with hell (Isa 28:15; Dan 9:27) to guarantee them "peace and safety." This is at the beginning of Daniels 70th Week, the the 7-year period that follows the Rapture.
The initial signs (Mat 24:4-10) the Lord gives correspond to the first five seal judgments (Revelation 6:1-11), which follow the catching up (4:1) and rewarding (v 10) of the saints of this age. The abomination of desolation (Mat 24:15) refers to the mid-point of the 7-year period (Dan 9:27b). The"great tribulation" (Mat 24:21) points to the last half of that period and the visible coming of the Son of Man (v 27) to the Lords return to earth. The teaching comparing the days of Noah (vv 37-42) relates to the coming of the Son of Man, referring back to verse 27, as does the warning in verse 44. The Parable of the Faithful and Evil Servants (vv 45-51) deals likewise with "His coming" which must be the coming of the Son of Man in the context.
The Parable of the Talents (25:14-30), which follows the Parable of the Ten Virgins, cannot refer to believers of this age. The wicked servant had responsibility entrusted to him by his master, yet is cast by the master into outer darkness. This, similar to the parable at the end of chapter 24 must have a Jewish setting. The prophecy of the sheep and the goats likewise refers to the Son of Mans coming in glory.
The context of the Ten Virgins is the Lords return to earth and not the Rapture.
Are the ten virgins a picture of backsliders and of Christians who are waiting for the wedding?
To draw teaching about a partial Rapture from this parable is ill-considered, because first the context shows the parable doesnt deal with the Rapture. Second, the descriptions of "wise" and "foolish" in this last discourse in Matthew remind us of the same contrast at the end of the Lords first discourse (chapters 5-7). There the foolish do not build on His sayings and their building suffers a great fall. They are not believers. Third, should anyone relate the waking (wise) and sleeping (foolish) virgins to the two states, "whether we wake or sleep" (1Th 5:10), the context in that passage will dispel the idea of a partial Rapture. Paul does describe Christians who are watching for the Lords coming and Christians whose behavior is like the unbelievers of the world (sleeping in the night, v 7), but he states the reason both will be saved by the Rapture from the coming wrath (during the 7-year period) is the result of the death of Christ and not of our spiritual condition.
Teaching of a partial Rapture is not in the Parable of the Ten Virgins or anywhere else in Scripture.
What is the interpretation of this parable?
The virgins all have lamps which indicate they are waiting for the return of a bridegroom during the night. This is their testimony. They are all unconscious of the time, for they are sleeping. In the middle of the night, a cry brings all of them to consciousness. The announcement is that this is the night time of the bridegrooms coming. The virgins are not a bride or bridal candidates. They are waiting to join the wedding feast (the context defines whether the word "marriage," v 10, refers to the wedding or the wedding feast) with the bridegroom. The event announcing the coming of the bridegroom shows the difference between the two classes. The others prove incapable of meeting him, because they have no oil to sustain their professed expectation of the bridegroom.
Two types of Jewish people profess to be awaiting the return of Christ to earth. In the middle of the 7-year period, the event the Lord describes in chapter 24, the abomination of desolation, takes place. The Lawless One desecrates the Jewish temple in Jerusalem by taking the place of God, in all likelihood sitting on the mercy-seat of the temple. This will cause those Jews who profess to wait for the redemption of Israel (Luke 21:28; 2:38) to recognize the crucial prophetic times surrounding them. Those who are not born of the Spirit (pictured by the oil in the vessels) will not be able to withstand the power of the Beast (the Lawless One) and to survive in a society governed by the mark of the Beast (Rev 13:4-18). When the Sun of Righteousness (Mal 4:2) comes to end that dark night of persecution, those regenerated by the Spirit will enter the joyous wedding feast (Rev 19:9, 11). The unregenerate will be eternally excluded from the kingdom and the presence of the Lord.
Does this teach a second chance of salvation after the Rapture?
Perhaps the question comes from the suggestion of the wise virgins that the foolish go to buy oil. Both classes are Jews who are waiting for the coming of the Bridegroom, the Son of Man returning with His Bride, the Church. The Lord does not give us their history (as to whether they had heard the gospel before the Rapture), but he does give us their heritage. They had the Old Testament prophetic Scriptures to assure them of the Lords return to earth in keeping with the signs, the times, and seasons. The issue of a second chance after the Rapture is not in this passage.