Well, the Greek Roman Empire was on the verge of collapsing several times between 800 and 1300 A.D. to the Persian Empire. The only reasons why the Persians keep getting repelled was because of reinforcements from the Roman Empire's territories in Aegypt, Cyrene, and Libya.
That said, the Persian Empire itself was on the verge of collapsing during the same period, yet somewhat surviving like the Roman Empire.
Knock out the Greek Roman Empire, and Southern Italy may eventually Latinize.