Wreckage (flotsam, jetsam, lagan and derelict) from a wrecked vessel, or a wrecked vessel itself, falls under maritime salvage laws, which in theory allow a salvor legal rights to the cargo and remains of the wreck (with various legal distinctions for the type of wreckage that I'm not an expert on, so I'll stop here.). Salvage is distinct from piracy, which is taking a non-wrecked or non-derelict ship by force.

As a practical matter, those laws were not well developed in the 17th and 18th century, and in certain regions such as the Caribbean of pirate lore fame, European laws were inconsistently applied and enforced. If one were to find survivors on a week, the ethical thing to do would be to drop them at the next port call, or make some effort to repatriate them to a friendly port, but how often that actually happened is probably unknowable.