I'm looking for low dropout three pin regulators that are designed for use when there is a voltage on it's output pin and power is disconnected.
Okay, well I'd say most if not all regulators can withstand that situation. Think about it: when power is removed, the output capacitor would basically be supplying 3.3V and the input cap would be open - yet almost (if not all) regulators are fine with this.Actually the input will be open, no voltage present. It's for a serial adapter where when built will have either an external power supply via the regulator or be used as a daughterboard on a 3.3V motherboard.
Adding a diode on the output pin would work BUT it would drop the output by 0.2V not desired.
I would think that you would not need a 4700µF capacitor on any modern regulator.The old LM78xx series needed a diode across the in & out pins. I would have figured modern regulators would have something similar built in.
And the input will not be shorted.