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When a p-n junction is forward biased then its energy-band diagram looks like this:

enter image description here

What would happen if $V_a>V_{bi}$? ($V_{bi}$ is the built-in potential and $V_a$ is the externally applied voltage). Apparently, the bands would "reverse", in the sense that the conduction band limit in the p-side will be lower that the conduction band limite in the n-side; the same would happen with the valence band.

What's the meaning of this? Can this happen?

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No the energy band would not reverse. As we increase the applied volatge the drop across the nuentral region increases such that the n side depletion region is always higher in potential to the p side depletion region.

Actually :

Depletion potential = (built in potential) -{(applied potential)-(potential drop across neutral region) }

But at lower applied bias the potential drop across the netrual region is negligible and gains prominence at higher applied bias.

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