a distinction ought to be made between power and action. For it is one thing to declare, that "it is possible for the faithful to fall away from faith and salvation," and it is another to say, that "they do actually fall away." This distinction is of such extensive observance, that even antiquity itself was not afraid of affirming, concerning the elect and those who were to be saved, "that it was possible for them not to be saved;" and that "the mutability by which it was possible for them not to be willing to obey God, was not taken away from them," although it was the opinion of the ancients, "that such persons never would in reality be damned." (The Apology or Defense of James Arminius – Articles 1 &2)
At first glance, the distinction seems simple enough. The statement “I can pick up this pen” is about my ability, the statement “I will pick it up” is about the future. Still, when it comes to the questions can vs. do true believers apostatize, it seems hard to believe the answer to one could be yes, and the other no. If we can, but no one ever will, does that impinge on the idea of ‘possibility’? Not really, if you hold to the foreknowledge of God (Matthew 26:53, Acts 27:24,31). That goes for all views of foreknowldge: Calvinists, Molinists and Simple Foreknowledge. But Molinists and Calvinists are in a possition to explain how this works; even though they have different ideas of possible. For example, here's what Francis Turretin (who was a Calvinists and a determinism and a compatibilist) had to say:
“The question does not concern the possibility of failing on man’s part and in a divided sense. For no one denies that believers considered in themselves as to the mutability and weakness of their nature, not only can fail, but could not help failing if left to themselves (especially on the approach of the temptations of Satan and of the world). But the question concerns the possibility of failing on God’s part, as to his purpose in the compound sense and with regard to the event itself. In this sense, we say that defection is impossible, not absolutely and simply, but hypothetically and relatively.” (Francis Turretin. Institutes of Elenctic Theology V2 p594)
Here’s Turretin's concept in action, used to explain scripture:
“The passage…(Ezk 18:24) does not favor the apostasy of saints. 1. It is hypothetical, not absolute; (bhshvbh tsdyq) “when the righteous turneth away” (i.e. “if he turneth away”). However, it is known that a condition puts nothing into being, but denotes only a necessary connection of the antecedent with the consequent. If some possibility of defection be denoted on the part of man (when viewed in a divided sense), it cannot at once be inferred that there is a possibility in the compound sense on the part of the grace of God and as to the event. For what is possible with regard to the nearest and known cause is impossible with regard to the remote and hidden (which is in the decree of God). Here then, where God prescribes to man his duty and acts as law giver, he does not disclose the event of the things decreed by him. “ (Francis Turretin. Institutes of Elenctic TheologyV2 p 612)
Here’s another statement about David, that takes it even a step further.
“It is one thing for a believer sinning grievously to be damnable by his own merit (if regarded as to himself in a divided sense); another, if considered in the compound sense and as to God’s decree. In the former sense, it is true that he is exposed to death and if he continues in that state, will certainly be condemned. But in the latter sense, it is rightly said that thy will be absolved and saved (God so arranging the matter by his immense love and wisdom that he may not die in that state, but may be restored and return to the way by a renewed act of faith and repentance before he reaches the goal). Hence according to a double relation, these two propositions (although seemingly contrary) can be true at the same time. It is impossible that David (elected and man after God’s own heart) can perish. It is impossible that David, an adulterer and murderer (if death should talk him away in his impenitence) can be saved. The former by reason of God’s decree; the latter by reason of the heinousness and demerit of his sin. But this difficulty divine providence and grace solves,taking care that David (or any of the elect) should not die in that state in which on account of impenitence he would be excluded from salvation.” (Francis Turretin. Institutes of Elenctic Theology V2 p614)
So for Turretin, looking narrowly at just man's weakness, apostasy is possible, but looking more broadly at man's weakness in light of God's protection, apostasy is possible.
On the other hand, here's how Molinists William Lane Craig explains it:
Congruism could maintain that God via His middle knowledge knows just what gifts of grace to accord in any possible world to each believer's will so as to elicit a continuing response of faith from that person. Hence, every believer will persevere to the end in whatever world he exists even though he is free and it lies within his power to reject any particular gifts of God's grace.
Such a Congruist doctrine of perseverance appears very paradoxical because even though the believer freely perseveres and is able to reject God's grace, nevertheless there are no logically possible worlds in which he apostasizes. Is such a doctrine coherent?
It does seem coherent, I think, for the Congruist to maintain that the believer freely perseveres even if he is not free to apostasize. That the believer freely perseveres is evident from the fact that for any particular congruent grace accorded him, there are worlds in which the believer rejects that grace. But via His middle knowledge, God in each of those worlds offers the believer some other gift of grace to which God knows the believer will freely respond. So even though there are no possible worlds in which a believer falls away, nonetheless believers persevere freely. The crucial point, once again, is that God's grace is only extrinsically efficacious, and therefore the believer's freedom is not causally constrained by God's action....
To maintain that the warnings of Scripture are the means by which God guarantees the perseverance of the elect is in fact to adopt a Molinist perspective. That perspective need not be so radical as Congruism. The Molinist who holds to the perseverance of the saints may regard (4) and (4') as false because, in counterdistinction to the Congruist, he holds that there are realizable worlds in which believers do reject God's grace and apostasize. That is to say, such worlds are not merely logically possible, but are feasible for God. But the Molinist who holds to perseverance will simply add that God would not decree to actualize any of these worlds, or even more modestly, that God did not in fact decree to actualize such a world. In the world He chose to actualize, believers always persevere in the faith. Perhaps the warnings in Scripture are the means by which God weakly actualizes their perseverance. That is to say, in the moment logically prior to creation, God via His middle knowledge knew who would freely receive Christ as Savior and what sorts of warnings against apostasy would be extrinsically efficacious in keeping them from falling away. Therefore, He decreed to create only those persons to be saved who He knew would freely respond to His warnings and thus persevere, and He simultaneously decreed to provide such warnings. On this account the believer will certainly persevere and yet he does so freely, taking seriously the warnings God has given him. (A Middle Knowledge Perspective on Perseverance and Apostolic Warnings)
So for the Molinist, God chooses a world in which He knew we can, but would not fall away.
So 'possibility', understood either the robust libertarian sense, or the minimal determinist sense, is quite consistent with the thing never actually happening. Thus both Calvinists and Molinists may, in their own ways, affirm that true believers can, but will not fall away. In fact, anyone who believes God uses His foreknowledge providentially could uphold this difference. For example, Charles Finney (who was neither a Molinist or Arminian) said:
Everything revealed in the Bible concerning the perseverance and final salvation of the saints, and everything that is true, and that God knows of the free actions and destinies of the saints, may be of this class. These events are nevertheless certain, and are known to God as certainties. Not one of them will, in fact, turn out differently from what he foresees that they will; and yet by natural possibility, they might every one of them turn out differently; and there may, in the only sense in which danger is predicable of anything, be the utmost danger that some or all of them will turn out differently from what they in fact will…..
2. It is not intended that saints, or the truly regenerate, cannot fall from grace, and be finally lost, by natural possibility. It must be naturally possible for all moral agents to sin at any time. Saints on earth and in heaven can by natural possibility apostatize and fall, and be lost. Were not this naturally possible, there would be no virtue in perseverance.
3. It is not intended, that the true saints are in no danger of apostasy and ultimate damnation. For, humanly speaking, there may be, and doubtless is, the greatest danger in respect to many, if not of all of them, in the only sense in which danger is predicable of any event whatever, that they will apostatize, and be ultimately lost.
4. It is not intended, that there may not be, humanly speaking, myriads of chances to one, that some, or that many of them will fall and be lost. This may be, as we say, highly probable; that is, it may be probable in the only sense in which it is probable, that any event whatever may be different from what it will turn out to be….
It is intended, that all who are at any time true saints of God, are preserved by his grace and Spirit through faith, in the sense that subsequently to regeneration, obedience is their rule, and disobedience only the exception; and that being thus kept, they will certainly be saved with an everlasting salvation. (Charles Finney’s Systematic Theology. Lecture XLVII - Perseverance of Saints)
The distinction between "cannot apostatize" and "will not apostatize" really helps make sense of passages that speak of salvation as conditional on perseverance (i.e. Matthew 24:13; Colossians 1:23; Hebrews 3:14; Revelation 3:5) and also warning passages like Ezekiel 18:24, Hebrews 6:4-6 & 10:26-29. Perhaps they are truly saying we can loose our salvation, but other passages teach that we never will. Of course, just because we can hold this view (i.e. there's no logical contradictions) doesn't mean we should (i.e. it's taught in the bible). So, God willing, we need to look at biblical passages about the future of believers. Since examples go beyond warnings, we also need to look at the alleged "examples of apostasy", such as David, Judas, the Israelites who rejected Christ, Hymenaeus and Alexander, and false prophets of 2 Peter 2 and Jude. This topic also naturally brings up questions about assurance of salvation and antinomianism which should be discussed.