Paul exhorts his spiritual son Timothy to wage the good warfare against Satan. How do we do that? By means of faith, and maintaining a good conscience. We build up our trust in Christ, so that it is a whole walk and not just a moment of conversion. A turning-point leads to a life. We learn to avoid sin, and also confess it when we commit it (1st John 1:9).
However, Paul and Timothy both knew some who had rejected faith and a good conscience. I believe these people are different from the people described over in Hebrews 3-4. In Hebrews 3-4, Paul exhorts certain readers who had not yet exercised faith in Christ to do so. He warns them not to be like the traveling Jews in the wilderness, just along for the ride, enjoying the benefits of Exodus deliverance but still worshiping their idols. In the end, they dropped dead under the wrath of God before they reached the promised land.
In this case, however, Hymenaeus and Alexander at one time had faith and a good conscience. I say this because you can't, in the strict sense, fall away from a belief you never had accepted; and more importantly, they had been members of the church (Paul says he delivered them over to Satan, which is very similar to his counsel about disfellowship in 1st Corinthians 5-6). This presupposes they had been baptized, since an unbaptized Christian church member in the 1st century was unheard-of.
Hymenaeus and Alexander hadn't been dithering indecisively around the gang-plank of Christianity. They were both already sailing, and then, by their own laziness and self-centeredness, they rejected faith and a good conscience, shipwrecked themselves. Paul holds out their example as something that can happen to any Christian, if we don't take the pains necessary to avoid it.
Paul doesn't speak to the question of their eternal destiny in the afterlife. He doesn't address "eternal security" here at all. If you want Paul to exposit here on security and assurance, you are disappointed. He made one simple point, which was a warning: for a Christian, spiritual shipwreck is possible. You cannot be assured that everything ahead will be smooth sailing. Your Christian life is not like a Tesla self-driving car.
The responsibility of building up your faith and godliness rests on you.