Yes, ABS-B on a 1090 extended squitter can be turned off by the crew, by switching off the transponder. Only ADS-B that is transmitting on a UAT (978 MHz) typically is ON as long as the Battery Switch of an aircraft is ON.
I think that in the future aircraft systems will be redesigned so that an ADS-B system never can be switched off. However, we don't know why the transponder stopped functioning. It could have been turned off manually, flown out of range, or malfunctioned maybe due to an electrical fire.