Ship is sunk when the last level is either hit with "Call Leviathan" or during a battle that the "sink chance" (Based on ship count) activates and the ship hits the sea floor.
Sea Floor or bottom is essentially limbo for ships with no owner. You can pull them up using a wreck hunting fleet.
This page will show how many ships are currently on the sea floor - https://s2.piratesglory.com/index.php?p ... tore=ships