In electrical circuit terminology, "open" means "not connected" while "closed" means "connected/shorted".
That's different from direct translation of Chinese (and I think several European languages) where "open the light" means to turn it on (by closing the circuit, naturally).
I think it's most common English engineering usage (by far) to say that a burned out lamp fails open [circuit].
If it failed closed then a bulb burning out would trip the circuit breaker.