No, Our Lord said that if any of the branches--which are saved people as defined by our Lord right in John 15--if they don't abide in the vine, they will be cut off and burned. The passage is plain, as is Matt 24:13.
Believe what you will, abiding in Christ is a characteristic of the true believer, although it doesn't make him a true believer, it is way to see who is who, "by their fruits you shall know them".
Galatians 5:19-23 shows us the difference between the works of the flesh and the fruit of the Spirit.
Anyone not abiding is Christ is not part of the true vine and indeed never has been and they cannot produce the fruit of the Spirit of Christ because they have not His root.
A phoney may give the impression of "abiding" and even be a proponent of "Lordship salvation (saying Lord, Lord!)" with works to prove it ("and in thy name done many wonderful works?)" but the disconnect is proven by Jesus statement "I
never knew you", in other words they were never His to fellowship with in the first place.
But in one thing you are correct "
they will be cut off and burned."
Matthew 13
40 As therefore the tares are gathered and burned in the fire; so shall it be in the end of this world.
41 The Son of man shall send forth his angels, and they shall gather out of his kingdom all things that offend, and them which do iniquity;
42 And shall cast them into a furnace of fire: there shall be wailing and gnashing of teeth.
43 Then shall the righteous shine forth as the sun in the kingdom of their Father. Who hath ears to hear, let him hear.
The wheat didn't turn into the tares. The tares were/are the children of the devil from the beginning. Jesus planted wheat, they remained wheat, grew up and produced fruit.
The evil one planted the weeds and they shall be burned.
HankD