Well, Once Saved Always Saved was originally an outgrowth of the way the early-sixteenth-century Swiss and South German Reformers (the forerunners of what we now call “Calvinism”) applied Augustine’s teachings. I think there was some influence from more radical theologies as well–a guy named Martin Borrhaus taught an almost Manichean view of “two seeds” according to which people came into the world already with light or darkness within them, and you see the influence of that pretty strongly in the early Reformed guys, until Calvin brought Reformed theology more in line with Lutheranism and with traditional Augustinianism.
But the key move was to take Augustine’s doctrine of predestination (which was the standard view in the West throughout the Middle Ages, with some modifications), link it up with sola fide, and then make this combination the basis of soteriology. That leads to “eternal security” or the “perseverance of the saints.” If faith is a gift of God, and those who have faith are saved, then it makes sense that only the elect would ever have real faith. That required them to abandon baptismal regeneration, but they might have done that anyway because of their tendency to rationalize and spiritualize sacramental theology.
The Reformed today will often distinguish their doctrine of perseverance from the watered down “once saved always saved” doctrine that you find among many American Protestants who aren’t real Calvinists. In the Reformed understanding, faith and works are linked by predestination. If God has chosen you to have faith, God has also chosen you to have works, and like the Lutherans they think that faith will inevitably bear fruit in works. So they don’t play down good works as some modern Protestants do.
But yes, penal substitution plays a role here as well, since in full-blown five-point Calvinism Christ only died for the elect, and so all those for whom Christ died (and only they) will come to faith, persevere in faith and good works, and be saved.