"Around 150 to 200 fiber-optic cable breaks are recorded each year. Between 65% and 75% occur in water depths of < 200 m and result mainly from fishing and shipping activities. In contrast, breaks attributed to geohazards comprise < 10% of the world average. However, seaward of the busy continental shelf and upper continental slope, geohazards account for at least one-third of breaks."
-- "Insights into Submarine Geohazards from Breaks in Subsea Telecommunication Cables"
They are designed with this in mind, and certainly hold up better than oil pipelines, which also have to be engineered to withstand earthquakes.
I expect it is unlikely for an earthquake itself to sever a cable, but knocking out power / knocking over a building that then destroys the cables landing site is possible, if rare.
