Good airlines don’t go bust in hard times. The time period 2008/2009 is one of the most problematic, as it had seen preposterous fuel prices and a sharp decline in demand, especially in business travel.

BA may have announced losses, we don’t know about cash flow. Announcing huge losses is normally no direct threat, I guess the board also uses these losses as leverage versus the unions.
I guess they have pretty healthy background, like many big fishes in Europe. Their American counterparts have much worse backing.

However, there gonna be casualties and it will not be funny.