The piston arm is able to be destroyed without destroying the base.
Steps to reproduce:
1. Build the setup in the first screenshot(a simple sticky piston-based redstone clock) ignoring the hopper and the dropper.
2. Place an item inside the chest.
3. The piston should now start pulsing on/off.
4. Aim for the piston arm and attempt to break it, you are likely to break the block instead, but if that happens just replace it and try again.
5. Once the arm is broken you will notice something like the screenshot 2.
Upon further testing I have discovered that this is not a client/server de-sync, therefore re-logging does not fix the piston, the only ways I seem to have found to fix the piston are:
1. Break it and replace it.
2. Toggle the existing power source that activated the piston when the arm was broken.
3. Place a block where the extended piston arm is supposed to be.
I have also noticed that in survival, if you place a block as stated in the third way to restore the arm, the block will be consumed, and will not be returned to the player.
Additional note: It does not matter whether the comparator is in subtraction mode or not.