Hear ye therefore the parable of the sower. When any one heareth the word of the kingdom, and understandeth it not, then cometh the wicked one, and catcheth away that which was sown in his heart. This is he which received seed by the way side. But he that received the seed into stony places, the same is he that heareth the word, and anon with joy receiveth it; Yet hath he not root in himself, but dureth for a while: for when tribulation or persecution ariseth because of the word, by and by he is offended. He also that received seed among the thorns is he that heareth the word; and the care of this world, and the deceitfulness of riches, choke the word, and he becometh unfruitful. But he that received seed into the good ground is he that heareth the word, and understandeth it; which also beareth fruit, and bringeth forth, some an hundredfold, some sixty, some thirty.
Clearly faith and works of faith (fruit) are intertwined. One who is saved must persevere. One who is saved must have fruit.
The seed is the Gospel itself, which is preached openly to all. But it is effectual only in the sheep of God. Hence why Augustine points out that the gift of perseverance is reserved only for the elect, while others necessarily must fall away:
But of such as these [the Elect] none perishes, because of all that the Father has given Him, He will lose none. John 6:39 Whoever, therefore, is of these does not perish at all; nor was any who perishes ever of these. For which reason it is said, They went out from among us, but they were not of us; for if they had been of us, they would certainly have continued with us. 1 John 2:19. (Augustine, Treatise on the Predestination of the Saints)
I assert, therefore, that the perseverance by which we persevere in Christ even to the end is the gift of God; and I call that the end by which is finished that life wherein alone there is peril of falling. (Augustine, On the Perseverance of the Saints)
Here is the verse Augustine is referencing in its full:
1Jn 2:19 They went out from us, but they were not of us; for if they had been of us, they would have continued with us. But they went out, that it might become plain that they all are not of us.
Any who belonged to Christ must necessarily stay, and those who leave are never described as having once been of us, but of leaving us at some point because they were "not of us" to begin with.