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If it has the ability to monitor battery life then it can certainly do stuff like emit an impeding dead battery warning tone and then gently decelerate to a stop.
Though I bet its an issue where the battery level is simply monitored via voltage. So lets say a 15% charged battery has enough current to push the rider along on level ground, BUT, the moment the rider hits an uphill, the current increases beyond what the now weaker battery can provide, the voltage drops below the battery threshold and the battery protection circuit shuts down. Very unsafe design.
A proper design would allow the battery and motor drive to cooperate so when the motor current demand rises to maintain velocity, the battery pack can tell the motor, sorry, I cant give you anymore and the motor drive can then decelerate or simply refuse to continue accelerating.