Depends on the jurisdiction. In many countries, yes there are insurance requirements. Even in ones where there aren't, most vessels owned by larger companies carry insurance for the same reason anyone else does.
On the other hand, since oceangoing ships are (mostly) regulated by the countries they're registered in, which is frequently a regulation-light jurisdiction like Panama, Liberia, or the Marshall Islands - there are a surprising number of situations where the owner of the ship just completely disappears and the ship is left to rot.
One of the most famous recent examples of this was the ship involved in the Beirut port explosion this year. After being impounded for being unseaworthy, it rotted at its moorings and eventually capsized in the Beirut harbor.
A quick trip through developing-country ports on Google Earth will have quite a few ships like this.
On the other hand, since oceangoing ships are (mostly) regulated by the countries they're registered in, which is frequently a regulation-light jurisdiction like Panama, Liberia, or the Marshall Islands - there are a surprising number of situations where the owner of the ship just completely disappears and the ship is left to rot.
One of the most famous recent examples of this was the ship involved in the Beirut port explosion this year. After being impounded for being unseaworthy, it rotted at its moorings and eventually capsized in the Beirut harbor.
A quick trip through developing-country ports on Google Earth will have quite a few ships like this.