OK, so it is true that to order aircraft you must have the required cash available for the order..correct? (i.e. there is not some way of ordering aircraft with a negative cash position that I am not aware of?)
Yes, you must have cash to order aircraft.
Successful airlines can have quite large negative values, if they have enough income and accumulate enough cash on hand to allow them to qualify for large loans, and then they spend the amount borrowed and some of the additional cash on hand on new aircraft. In MT3 I've had negative values below -20mil and I'm hardly the highest earning company in the game. I've never had a negative cash position.
The other possibility, of course, is that the airline with ~-50mil placed the aircraft orders before they started losing money and is now in the process of failing...