CONCLUSION
Unfruitfulness is a consequence of not abiding, and while one abides they bear fruit and this ceases when they stop abiding.
The whole point of the passage is to encourage the disciples to abide, to remain in Christ. This would be pretty irrelevant if they can't but abide and bear fruit. But there is the risk of failure to abide resulting into unfruitfulness and casting away, withering and being cast into fire.
Your conclusion is wrong, because you assume to understand what "abiding" means here.
Coming from a L.O.S.T. (loss of salvation teachings) viewpoint, which demands men collaborate with God to get salvation accomplished, it is understandable that you would impose a meaning of "remaining faithful" to the abiding Christ speaks about here.
But here is what you are forgetting to do, just as you do when you enter the Book of Hebrews: you forget the significance of Historical Context.
Here is the vine which is not the True Vine, Vooks: Israel.
Israel looked to Covenant relationship as the means of provision, first, in relationship with God, then, those things needful to man. The Covenant of Law provided a means by which men might be in relationship with God, and...live.
When Christ states "I am the True Vine," what He is saying is that He is the source of provision.
(The Creation of) Israel provided relationship with God, Christ provides true relationship through Reconciliation, which the Law did not provide.
Israel provided sustenance for life (i.e., manna, the land, safety, et cetera), Christ provides Eternal Life.
When Israel failed to be in relationship with God, they were judged. This is what the Lord means when He says "I am come to the Lost Sheep of Israel only," He is saying they were in a state of destruction. The word "lost" is the same word used when the Lord state "Fear Him Who hath power to "destroy" both soul and body in Hell."
"Abiding" in this context, therefore, refers to that approaching time when those of Israel would make a decision to remain in the provision of God or to not remain. When the New Covenant was established, the previous provision became obsolete, and is not considered to bring relationship with God.
This is why we do not find the disciples of "not abiding," because at this point the revelation of the Mystery of the Gospel of Christ has not even been brought to them. An example of this is found in Matthew 16:21-23 where, having received the Gospel of Christ from no less than Christ Himself...Peter says "This shall never be unto thee, Lord."
So the abiding in view has a foremost application to Israel, rather than a general teaching that supports the L.O.S.T. (loss of salvation teachings). We can apply a general principle to those who associate with Christ who profess faith in Christ then fall away. But, they are branches, not because they are saved (and they are not saved in John 15 under New Covenant provision), but because they are of Israel.
And that is why we see that the Lord, as He said, was sent only to the Lost Sheep of Israel, not the Gentiles, not the Samaritans. Because the Gospel of the Kingdom had a primary relevance to those the promises were given.
God bless.