The perfect passive infinitive in an indirect statement may occur with fuisse rather than esse; this is rare and, in fact, is generally not listed in verb conjugations, but should at least be recognised.
The perfect passive infinitive with esse refers to an event which took place before the verb of speaking.
[i] Nuntius dīcit ¦ urbem captam esse. │ The messenger says that the city was / has been captured.
[ii] Nuntius dīxit ¦ urbem captam esse. │ The messenger said that the city was / had been captured.
Occasionally, however, you will come across the perfect passive participle with fuisse which emphasises that a situation had existed at a certain point in the past before the time of speaking:
Ex ōrātiōne appāret … exercitum in forō collocātum ā Gn. Pompeiō fuisse (Asconius) │ It appears from the speech that the army had been placed in the forum by Pompey
Satis est … docēre … magnam spem in Milōnis morte prōpositam … fuisse (Cicero) │ It is sufficient … to show … that great hope had been placed on Milo’s death
Populum Tanaquil adloquitur … sōpītum fuisse rēgem subitō ictū (Livy) │ Tanaquil addressed the people, [saying that] the king had been rendered unconscious by a sudden blow
Note the inclusion of ‘previously’ and ‘formerly’ in the following translations, emphasising the function of fuisse.
Cognōvī tibi eum falsō suspectum fuisse (Cicero) │ I found out that he had previously been unfairly suspected by you
Zanclē quoque iūncta fuisse dīcitur Ītaliae (Ovid) │ It is said that Zancle had formerly been joined to Italy