There were several SIBYLS on the Greek side of things and many prospered under the Romans too. The SIBYL-OF-CUMAE underwent an inspired revival under the Romans after almost fading away under the Greeks.
She grew in stature and was restored to former glory at the age of 700. She wrote nine books of prophecies and tried to sell them to a King Tarquin.
He refused to meet her price, so she burnt three, offering the remainder at the original price. Again he refused so she burnt three more.
Finally realizing she was not bluffing, he paid the full price for the last three and she went away cackling.
Nobody understood a word of the surviving books, and we suspect the King had merely bought three volumes of indexes, footnotes and corrections for the first six books. We know how he must have felt: trying to complete a set of secondhand books is fraught with peril and disappointment.
However, the remaining books of prophecy did manage to cause rumor and intrigue in the Roman Empire for quite a while. Legends sprang up asserting that So-And-So Caesar was predicted to die — and there was generally someone around willing to oblige.
Sybil herself wisely vanished without trace. Rumors that she now works for the Godchecker Oracle are mostly unsubstantiated.