It sounds like working for a self-insured company is strictly worse for employees than working for a company that offers insurance through an insurance company, risk-wise.
Not "strictly worse", because if one cares about maximizing profits for the company and wages for the employees, the self-insurance route might be better overall. Formal insurance arrangements can be a real drain on resources. On the other hand, some companies choose to self-insure without fully appreciating the risks.
How serious are the risks to the company's other assets? Can a company limit the damage to its other assets if the money it set aside for insurance gets used up?
> Can a company limit the damage to its other assets if the money it set aside for insurance gets used up?
Yes, but at risk of civil lawsuits from the insured, who might have a different perception of their coverage. This kind of thing actually happens, often based on an implied contract between the employer and the staff that may have never been fully committed to paper.