The Greek word is apostasia which means “to defect or depart from the truth,” or “to forsake or revolt.” It is where we get the word “apostasy.” This falling away from the truth is an increasing departure that will culminate in full blown apostasy after the departure of the true church and only the presence of the harlot church on earth. The final act of apostasy will be the false prophet causing an image of the beast to speak in the rebuilt temple [abomination of desolation].
Jesus described this apostasy in the tribulation in Matt. 24:10-12, “And then shall many be offended, and shall betray one another, and shall hate one another. And many false prophets shall rise, and shall deceive many. And because iniquity shall abound, the love of many shall wax cold.” In this passage he gives the character of man’s heart when restraint is removed. This spiritual treason reveals an unregenerate heart. They give evidence they were never saved [v. 13]. The guarantee of perseverance is built into the New Covenant promise, “I will put My fear in their hearts so that they will not depart from Me” [Jer. 32:40].
The Bible teaches that true Christians will persevere in the faith because they are kept by the power of God [1 Peter 1:5]. Those who fall away prove they were never truly believers to begin with [1 John 2:19]. Yet, the Scriptures do warn the believer from falling away in such passages as [Heb. 10:23, 26-29; Rev. 3:11], but true believers will persevere [John 10:28, 29; Rom. 8:28-30, 31,38, 39; 1 Cor. 1:8-9; 15:57-58; Col. 1:22-23; Phil 1:6; 1 John 2:24; 5:13].
Matt. 10:26-39 is talking about a false faith that does not continue. The people that the writer of Hebrews is talking are those who fall away or defect intentionally. Apostates hear the gospel, understand the gospel, but turn when they are on the verge of belief.