Specifically mentioning after the Great Fire to give the best chances.
I would note that Rome (and pretty much every city) in the ancient world suffered major fires. This is inevitable when you have heavy usage of wood in structures and the usage of fire for cooking/lighting. The Great Fire is notable because it destroyed so much of Rome in one go.
We know that some non-monumental buildings were re-used but I don't know any that would survive almost a millennium of usage. There's one mansion built in 120 CE that was repurposed into apartment blocks in 200 CE and by the early 4th CE it was turned into a single house. Around the 5th CE it was turned into a church (SS Giovanni e Paolo) - and that's the likely reason it survived. Being turned into a church is often why ancient structures survived the ages in better condition.