The sense if clear from context, but for the life of me I don’t see why γενομένην is feminine accusative singular. I would have expected the neuter. Suggestions?
πολιορκίαν γενομένην? I don’t know, but feels like it’s still accusative in agreement with the last phrase, and maybe the period before could be taken out, and the punctuation made a little more creative?
δεδεμένον doesn’t make sense without the preceding: καί με διὰ φυλακῆς Οὐεσπασιανὸς καὶ Τίτος ἔχοντες ἀεὶ προσεδρεύειν αὐτοῖς ἠνάγκασαν τὸ μὲν πρῶτον δεδεμένον . . .
As for γενομένην, here’s what a recent dissertation on Josephus has to say:
Barclay in his translation, like most modern editors including Thackeray, omits the orphaned γενομένην, which does not appear in all manuscripts and which is untranslatable with this punctuation, but could otherwise possibly be construed with πολιορκίαν (see Gutschmid 1893: 409).
porphyrios is obviously right about the beginning of the sentence being cut off in Barry’s extract; that’s clear from the excerpt itself. But even so I don’t see any way of making sense of γενομένην here, whatever the punctuation. Perhaps there was a second exemplar in which γενομενην stood directly after πολιορκίαν and was added in the margin of the primary exemplar, then got displaced in the process of collation. Otherwise it must simply be intrusive, but that would be extremely hard to explain.