If modern smart meters are anything like classic mechanical meters, they have a counter of the total amount of power consumed so far, and the power company bill

If modern smart meters are anything like classic mechanical meters, they have a counter of the total amount of power consumed so far, and the power company bills the difference between the current reading and the previous month's reading. Which means that, once the meter can be read again, you will be billed for all the power consumed in the meantime.