oh boy!
I'll give you some thoughts first so every one can begin shooting.
This is based on the theory of a future rapture followed by a future tribulation.
First question about people being saved after the rapture:
--Church age is Revelation chapters 2 and 3.
--Rapture and glorified Church in Heaven is Revelation chapters 4 and 5.
--Tribulation begins in
Revelation 6 and continues until Jesus returns with His church in
Revelation 19.
--A group of Jews described as 144,000 with the Father's name in their foreheads and made up of 12,000 from each tribe are found in
Revelation 7:1-8; 14:1-5) and a group of gentiles described as "a great multitude, of all nations and kindreds and tongues" in
Revelation 6:8-9 and 7:10-17 would be what we call the "tribulation saints."
Second question about God "removing" His Spirit when He removes the church at the rapture. I assume you are referring to
2 Thessalonians 2:1-10. Some pre-trib dispensationalists teach that there is a reference here to "the antichrist" who cannot be revealed until "he who now letteth will let until he be taken away." "He who now letteth" is seen as the Holy Spirit in the Church and at the rapture the Holy Spirit will leave when the church leaves. Some teach that the "falling away" or "departure" or "apostasia" here is the departure of the church or the rapture. Will the Holy Spirit "leave" when the church leaves? Well, He can't actually leave because He is omnipresent so He will still be here in His "omnipresence" but perhaps not in his "manifest presence." However, it seems to me that if there are folks preaching the gospel and folks accepting the gospel and folks laying down their lives for the Lord, the Holy Spirit must still be active and working among, upon, and within them.