The shipping company doesn't own the cargo, but I've read speculation that the creditors can seize the ships, then demand payment to unload the cargo, and if they don't receive payment seize the cargo to discharge the "debt". I don't know how a bill of lading would work in that situation, where the creditor wasn't the original party that the customer signed a contract with, and I'm curious how much latitude a creditor has in situations like these to abrogate previously-entered contracts.
It's really complicated. There are articles by lawyers.[1] There are many countries involved, with very different bankruptcy laws. Much of this involves admiralty law, which has a very different order of priority of creditors than regular bankruptcy law. Lawyers are struggling to figure out all the conflicts of law.[2]
Obviously if the cargo has any value, then the result is simply a higher freight cost than originally expected.
Yes, it is likely that cargo owners will have to pay extra to get their cargo delivered where they want - they have paid for a service, Hanjin won't provide that service, and anyone else will require payment for that same service. Even if the service (or a part of it) is practically unavoidable e.g. the cargo is at a ship and needs to be unloaded, so someone needs to pay for the loading. Maybe they have insured that, maybe not, but they can get their cargo anyway if they want.