> so these ships are abandoned by the companies that own them, with the crew still on board? and then the crew is just stuck there with dwindling food supplies until somebody comes to rescue them?

Yes, basically. The situation is really really nasty, every year thousands of sailors are stuck aboard abandoned ships [1][2]. Sometimes, crews get stuck for years [3] - and the situation is made worse by the fact that leaving ship means forfeiting payment.

[1] https://www.voanews.com/a/fleet-of-abandoned-ships-is-growin...

[2] https://www.bbc.com/news/articles/c3r4nr2zy2do

[3] https://www.bbc.com/news/world-middle-east-56842506