When accidentally leaving the battery switch or something powered by the hot battery bus on over night, an aircraft's battery could completely discharge. Normal startup, where the battery is switched on first and then external power is connected, would no longer be possible.
Is it possible to somehow connect an external power unit to the aircraft such that the drained battery is being recharged? Or would maintenance have to swap out the battery or charge it in some other way?
Details for the Boeing 737 are below, but answers for other airliners are welcome:
On the Boeing 737 NG, the batteries are charged via their own transformer rectifier units:
Battery Charger Transformer/Rectifier
The purpose of the battery chargers is to restore and maintain the batteries at full electrical power. The main battery charger is powered through AC ground service bus 2. The auxiliary battery charger is powered through AC ground service bus 1.
(Boeing 737 NG FCOMv2 6.20.12 - Electrical - System Description - DC Power System)
These ground service buses can be turned on independently of the main aircraft AC buses:
For ground servicing, a ground service switch is on the forward attendant’s panel. The switch provides ground power directly to the AC ground service busses for utility outlets, cabin lighting and the battery charger without powering all airplane electrical busses. The ground service switch is a momentary push button and is overridden when both AC transfer busses are powered.
(Boeing 737 NG FCOMv2 6.20.2 - Electric - System Description - Electrical Power Generation)
This sounds like the battery chargers could be powered via ground power in ground service mode. It is however not clear to me, if this push button would even work without any battery charge left.