Very big slow moving ships with massive spindles of weighted cables that verrrry slowly roll the cables out that sink down to the bottom. Maintenance is handled either by diving technicians or aquatic drones. Generally they hook a grapple line on the cable and hoist it up, cut the bad part out, and splice together. For the really deep stuff where that’s not possible they’ll pull the two ends up at the deepest parts they *can* reach, pull the now detached piece up, and either find the fault, repair it, and resplice, or splice a new length in.
Why don’t aquatic animals damage them? They totally do. Sharks like to take a bite out of internet infrastructure. We’re not entirely sure why.