When a business owner dies, it usually goes to the next of kin to take control. If there is no next of kin, I would imagine they'd find someone else from the family. If there is no family or next of kin in any way, I don't necessarily know what would become of that business. It could be taken in by the state, which will check into it and see what the next best steps would be.
I imagine whoever was under you, would take control of the day to day stuff, but I don't know who would take ownership if there is no next of kin.