The corporation that takes the union's role would be owned by the workers; that's the whole point. It would be more like a "worker's cooperative" from that point of view, the way unions as they currently exist are supposed to be, but it would be a corporation from the point of view of other corporations who wanted to hire organized labor, so it would be in a better bargaining position than unionized employees are today. The workers would come to a consensus as a cooperative on things like how the corporation would manage the business risk of unscheduled absences, and then the corporation owned by the workers would sell the service of organized labor to other corporations that wanted it, probably with various different service levels depending on things like how critical unscheduled absences would be, and with higher service levels costing more.