The twist in this tale is that Phoenician may have survived into the 11th century AD! Al-Bakri (whom I've mentioned before) enigmatically says of the inhabitants of Sirt in Libya that:
لهم كلام يراطنون به ليس بعربي ولا عجمي ولا بربري ولا قبطي ولا يعرفه غيرهمThe location (in eastern Tripolitania) is about right for it to be Punic, and if it were Greek you would expect him to know, considering he cites (more or less correctly) the Greek etymology of طرابلس (Tripoli) in the next page. So was Punic still spoken in the 11th century? Your guess is as good as mine, but it looks plausible.
They have a speech in which they jabber which is neither Arabic nor Ajami (by which he probably means Latin
but might mean Persian) nor Berber nor Coptic, which no one but them knows.