Moving the series resistor to the bottom does not alter the basic functioning of the shunt regulator. The output is still monitored for perturbations and active shunting device acts to counter those perturbations to yield a stable output voltage. Furthermore, because we now have a ready negative power supply, biasing the shunting tube becomes easy. All that is needed is a few additional resistors and a potentiometer. Additionally, the negative power supply is useful when setting up a zener diode string as a voltage reference, as the end of the zener string must be at the negative bias voltage of the shunting tube.
   But the inverting the shunt regulator topology  has at least one more advantage: the use of cathode resistor in the filtering of the power supply. In the conventional shunt regulator topology the cathode resistor is a liability, wasting heat and requiring an additional capacitor to shunt the cathode to ground. But in the inverted shunt regulator, this resistor is just part of series resistor, Rs, total resistance. The cathode does not need a AC path to ground because it is the ground.

Grounded Grid Amplifier
Shunt Regulator Front-End
     One tube is seldom enough. Even the highest transconductance triode has a paltry amount of transconductance compared to a solid-state device, such as transistors or MOSFETs. And it is transconductance, the change in current flow due to a change in grid-to-cathode voltage, that powers a shunt regulator. Adding a first stage of voltage gain effectively boosts the Gm of the shunting tube by magnifying the error signal at the output. One stipulation is that the extra gain stage cannot invert the phase of the error signal, which leaves out the grounded cathode amplifier, but not the grounded grid amplifier. This circuit is a real sleeper: it does not invert the input signal phase and offers a wonderfully high-frequency bandwidth, as its grid shields the plate. The downside to this circuit is its very low input impedance:  (Ra + rp) / (mu + 1).