Paul mentions three literal shipwreck experiences in 2 Cor 11:25 using the verb vauagein and these do not include his experiences narrated by Luke in Acts 27-28. What kind of work he was engaging during these three experiences remains completely unknown. The only other New Testament context in which this verb occurs is 1 Timothy 1:19. Here Paul used the verb metaphorically to describe how some believers “have experienced wreck on the rock of the faith (peri…enauagēsan),” i.e. they not longer followed Jesus according to the true Gospel. Mounce (Pastoral Epistles, 67) marshals the evidence that indicates the prepositional phrase with peri should be taken with enauagēsan (cf. 1 Tim. 6:21; 2 TIm. 3:8; 2 Tim. 2:18). He translates “shipwrecked the faith.”
Philo used this verb several times. When he describes his role in the Jewish Legation appealing to the Emperor Gaius for protection from the pogroms in Alexandria, he warns that if the emperor fails to act, the Jewish community will be “first upset, then shipwrecked (vauagēsei), then sunk to the very bottom” in regards to laws and rights which currently they enjoy (Leg. 371). He continues in the same vein using words like “waterlogged,” “dragged down,” and “submerged in the depths.” In an extended discussion of the uncertainty of life, Philo used the example that “some who embarked in summer, the safe sailing season, have been shipwrecked (enauagēsan); others who sailed in winter, expecting to be capsized, have reached the harbour in security” (De Jos 139). Similarly he speaks of sudden and unexpected evils by employing this example: “For many a time and to many has it happened that they have crossed wide spaces of navigable waters and passed a long voyage in safety escorted by favourable breezes, and then in the harbour itself have suddenly been shipwrecked (enauagēsan) just when they were on the point to cast anchor” (De Somn. II. 143). He then applies this morally to humans who have lived appropriately for many years and then suddenly “at the very eventide of life they have been wrecked on the rock (nauagēsantas…peri…peri…peri) of an unlocked tongue or insatiate greed of belly, or uncontrolled lasciviousness of the lower-lying parts” (De Somn. II.147). Philo laments the common human experience of living with exuberance and confidence because of momentary prosperity, when suddenly our lusts take control and “we strike the rocks and wreck the whole bark (enauagēsōmen + dative case) of the soul” (Mut. 215). We see Philo, as Paul using the term both literally and metaphorically, particularly with respect to moral/religious behaviour.
What is helpful is that the grammatical formation used by Philo at De Somn. II.147 nauagēsantas…peri is the same one used by Paul in 1 Timothy 1:19 peri…enauagēsan. In De Somn. it is immoral activities that cause personal destruction, whereas in 1 Timothy the people are shipwrecked “on the rock of the faith.” Philo also seems to use this expression with a sense of surprise. Those who embark have no intention to experience shipwreck — it catches them by surprise. Perhaps Paul has this sense of “surprise” in mind in 1 Timothy 1:19 as well. Mounce’s translation perhaps does not take account sufficiently of the presence of the preposition peri. This verb in Greek is intransitive and does not take a direct object normally.
In Hellenistic Greek we do find a few examples of the formation vauagein…peri. For instance, in the third/second century B.C. Philo Mechanicus in his Belopoeica describes how “things perforated experienced shipwreck around the place of rocky caves” (vauagein peri ton tōn choinikidōn topon). Diogenes Laertius (3rd century A.D.) describes how someone “was shipwrecked around the Coan Sea (tou de peri tēn Kōian thalassan nauagēsantos)” (Vit. Phil.1.31.9). Athenaeus Soph (late second century A.D.) in his writing “The Learned Banquet” (Deipnosophistai (epitome) Vol. 2.1, page 108, l.14) refers to Phorbas, her daughter and her sister who were “shipwrecked around Schedia” (nauagēsas…peri ton kaloumenon Schedian). Schedia was the name of Alexandria’s port town. Although these examples are not plentiful, they do suggest that the meaning of Paul’s expression in 1 Tim. 1:19 is that “the faith” is the element against which or around which the shipwreck occurs.
If this is a correct understanding of this expression then Hymenaeus and Alexander have experienced shipwreck, i.e. ruined their spiritual development, around or on “the faith.” It is not “the faith” that is experiencing shipwreck. The logic seems to be that these men, by altering the essential Gospel come under God’s curse and thus have destroyed their spiritual relationship with God “on the rock of the faith.” instead of “the faith” being a foundation for life and hope in God, it has become the shoal on which their false religious ideas will founder. Their false teaching has led them intentionally or unintentionally to “blaspheme” the true gospel. They will be proven wrong and God will demonstrate that he is right. All that Paul can do in this situation is “hand them over to Satan” with the hope that in some way God will act in mercy to rescue them.