I think FlyingDutchman missed a key part of your story: you can't just list for a flight on KLM like you would for a Delta or NWA flight.

You need to get a Zed fare for travel on KLM - which you can only get as the employee, spouse, parents or dependents (depending on airline - each is different on who can use a zed fare).

What is your relationship to the person who works for Delta/NWA? If you're furloughed, I can't see how you could get a zed fare, as it says for "Active Employees".