I am not a lawyer, but I am in the finance-related industry and I would say that there certainly is an angle for a lawsuit if someone really wanted it. This is just a theory. I am not advocating it, but essentially all you would have to do is become a shareholder of the Corporation and then sue under the premise that management was not operating the airline in the best interest of the shareholders. This is not an easy argument to prove. You would need hard facts. Not just anectdotal quips of people leaving. You would need to hire a firm to calculate the lost revenue, profit, etc. as a result of management's actions.
I suppose it is also possible that by some loophole you could also be considered a stakeholder if you have any miles in your DM account. Then you wouldn't even need stock.