Does the Holy Spirit leave people when they renounce their faith in Jesus?

This is a complex question. That being said, my assumption would be that the person was never actually saved. The person who renounces Jesus, according to Hebrews 6:1–8, was never in relationship with God in the first place. They are called “apostates” or “antichrists” (see 1 John 2:18–20). In such a circumstance, the Spirit did not leave because the Spirit never was in the life of this person. If this person was a believer, the Holy Spirit would not leave, but the Bible tells us we can grieve (Eph. 4:30) or quench the Spirit’s power (1 Thess. 5:19) even as believers.