How to store/use energy that could be generated from a solar cell duing the off stage of a buck converter?
By off state, I'm assuming you mean the part of the cycle where the buck converter is not feeding current into the buck converter.

If you look at the circuit you've shown above, you see two similar sections on the input and output, formed by an inductor in series and a capacitor to ground. This is a low pass filter, which basically lets DC through, but the high frequency AC from the switching section is heavily attenuated. What this means is that while to the transistor in the middle, it looks like the load on the supply is a high frequency square(ish) wave, to the solar cell it looks like a steady load, with only a minor ripple. The same thing happens at the output, the load receives an almost constant current or voltage, while the middle of the circuit sees high frequency AC.