What happens if my employer either goes bankrupt or goes out of business during my workers’ compensation case?

Fortunately, a business going out of operation should have no impact on the workers’ compensation case at all. The reason for this is because, just like in an automobile accident case, once the workers’ comp case is filed, we’re generally dealing with the workers’ compensation insurance company, not the employer.
You still were covered by insurance as of the date of the injury; it wasn’t canceled at that point. Therefore, regardless of what occurs with the business, the workers’ compensation case can proceed.
One positive from a workers’ comp standpoint is that if the business goes out of business while you are out of work recovering, they will not have the opportunity to bring you back to work on light-duty job status, so you may be able to continue receiving benefits for a longer period of time and have more time to heal.