As all of us know, there's pre defined shapes of all positions for different scales (major, minor, pentatonic, diminished etc.). However, what happens when u use (drop c, drop d, drop b) tunings.

I am sure the positions of notes certainly change, and the pre-defined shapes won't work. What one has to do then?
yeah the string that you change will have the pattern change.

an example,

in standard (EADGBE) if you play an Ab, it will be on the 4th fret of the E string.

but if you are in a drop tuneing say (DADGBE) that Ab will now be on the 6th fret.
Dropped tuning allows you to hit a minor 3rd inside your power chords(half-bar or 5th chords)A half step up from where your octave usually is, in standard tuning
e-x A G power chord with a minor 3rd
As far a scales go, I only use them for practice. When improvising, I just try not to use the low string and play the pattern the same (as you would in standard) on the rest of the strings.