So emergency crews would arrange a boat to fetch the crew on the life boat and a helicopter to grab anyone in dire need. Depending on your proximity to land and your region. You’re looking at either the military or coast guard doing this.
If people need rescued on the sinked ship they dispatch people trained to go into it and search. They use various tools to help narrow it down.
After a few days there’s special groups that specialize in body recovery that go in looking for the dead. Assuming it’s safe, at a certain depth they are considered lost at sea and left there.