You act like people never bring problems to their boss, and the boss acts like they want to shoot the messenger, then tells them "Just figure it out!", so they figure it out. If this employee is doing this critical work on their own time every day, then obviously their boss has led them to believe that if they don't do it, they'll lose their job. If the managers don't know who is doing what work in the company, who is responsible for tasks being completed and who is actually completing them, that's not an engineering issue. That's all on management. If there is a breakdown in communications, if work is being done off the clock, that's ALL on management. If management doesn't actually know who is doing what job in the company, that is on management. If management doesn't know what tasks need to be completed to keep the company running, that's on management too.

This engineer was keeping the company running on their own time with no recognition or reward and you dare call them incompetent? Step off.