The modem contains a single-core ARM CPU running a Linux-like OS.
The OS on the phone needs to task the OS on the modem to shutdown, when the OS on the phone is being shutdown.
In both OS, power is connected to the phone hardware (other than modem) and modem hardware even when both are shutdown. If both OS are shutdown, then neither is using power or using the battery or causing the battery to drain. There have been cases when the phone OS has shutdown while leaving the modem OS running causing the battery to drain.
The OS on the phone needs to task the OS on the modem to shutdown, when the OS on the phone is being shutdown.
In both OS, power is connected to the phone hardware (other than modem) and modem hardware even when both are shutdown. If both OS are shutdown, then neither is using power or using the battery or causing the battery to drain. There have been cases when the phone OS has shutdown while leaving the modem OS running causing the battery to drain.