There's really nothing wrong with your logic, but unfortunately it doesn't work that way. These ships are usually abandoned at port, which means what happens is subject to the laws of the country they're in. Most countries have laws about ships and shipping to prevent becoming responsible for abandoned ships, it's common for some crew member to be criminally liable for abandoning a ship at port. Then you take into account bankruptcy filings in the flag country with assets worldwide, it would be very hard for a person to claim a ship as salvage in territorial waters while litigation about assets is ongoing.
Ideally it would be as simple as you say, but when you're talking about potentially billions of dollars in machinery and cargo, owned by probably hundreds of different interests, the people on these ships get caught in the middle of the mess and nobody with a financial interest in the situation wants to help the poor saps take their money from them.
Ideally it would be as simple as you say, but when you're talking about potentially billions of dollars in machinery and cargo, owned by probably hundreds of different interests, the people on these ships get caught in the middle of the mess and nobody with a financial interest in the situation wants to help the poor saps take their money from them.