They will just buy insurance, and the insurance companies will figure it out.
It's not that simple.
Yes, premiums will adjust depending on the finances of the carrier but the cost of insuring the risk itself is quite variable and can be ruinous. The value of a delayed shipment of iPads is much higher than a delayed shipment of board games, yet Apple can tolerate the former while the latter could sink a company. The board game company might not be able to afford to insure the risk, even though the premium could be lower.
The fact is an Apple can manage the risk by spreading the load (they already do it multi modally, and probably already do it for ships too). A small company with one container or less of goods, cannot.
[1] http://www.chinalawblog.com/2016/09/hanjin-shipping-and-arre... [2] http://www.mondaq.com/unitedstates/x/528816/Insolvency+Bankr...
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.