Boost operation in inverting Buck-Boost converter
During the on state, the power supply charges the inductor.

During the off state, the supply is disconnected entirely from the inductor. The inductor's energy is delivered into the load, at a voltage determined entirely by the load. Therefore the load voltage can be lower than the input (buck), or higher than the input (boost), it really doesn't matter. The description buck or boost is not really relevant, as the same topology handles voltage increase or decrease.

Ultimately the load voltage is servoed by controlling the power into the load, which is the same (neglecting losses) as controlling the power into the inductor. This is done by controlling the inductor pulse on time, pulse frequency, or both.