I have heard that the Holy Spirit will not indwell believers after the Rapture. Will His work cease during the tribulation?
The Bible never says the Holy Spirit will be removed from the earth at the time of the Rapture. Some assume that the Restrainer of II Thessalonians chapter two is the Holy Spirit, but even if it is, all this passage of Scripture is saying is that the Holy Spirit will not be restraining lawlessness. It does not say that He will be removed from the earth.
The Holy Spirit will still be regenerating people after the Rapture, indwelling them, empowering them, etc. What He will no longer be doing is baptizing them into the Body of Christ since the body at that point will no longer be here on earth. It is more correct to say that the Holy Spirit will not baptize people into the Body, but He will still be indwelling people.