In the UK you can actually legitimately get two passports if you can show you need it for work (I think it's typically for travelling to countries who don't like each other and won't let you in if you have stamps from the other one). I wonder if this would count.
Or if you have dual nationality, You could use your other one.
Really though, most embassies will issue travel documentation if your passport is lost without too much difficulty ( it is effectively lost if you cannot get access to it).
If that sailor really wanted to leave, he can get another one from his embassy. This is more power dynamic between employee/ employer , I have seen similar stunts pulled by agents who get foreign workers in middle east.
