It is a bit difficult to tell what you mean by "Greece" ceasing to exist, since before Roman conquest it was not a unified state but a patchwork of kingdoms, leagues/alliances and independent city-states, as can be seen in this map depicting the area around the Aegean in about 200 BC. During and after the conquests there were some city-states which did become semi-autonomous protectorates, but this was never the case for all of Greece, and parts also belonged to the Kingdom of Macedon which became a province relatively early. Not to discourage more answers, but you can read some earlier threads on the Roman conquests of Greece like this one by u/nikephorosBasileu, this one by u/LOSS35 and this one by u/sapere_avde