Could you contact the conglomerate and inquire about their intentions for the domain? I have had people call me regarding domains I had for my recently sold well established company. While it was not a conglomerate, I appreciated when I received calls and would get back to the inquirer and let them know if they could or could not use it.
This however defeats your intention of profiting from perhaps a mistake on their part. Like DK and EastCoast said their are too many reasons not to do it unless you can get written permission from the conglomerate.