Dropout voltage will be around 200-400mV ( from the datasheet) so it will simply feed through the input less that. A big caveat though is the current drawn by the regulator through the ground pin will suddenly be a lot higher than the typical current, as it will be drawing the maximum current possible to turn on the output PNP pass device as hard as possible trying to stay in regulation. This can be an issue as it may be 100mA or more, and will often be the highest current in the circuit. If you can get a LDO that uses a MOSFET to regulate the ground pin current will not be as high when it drops out of regulation.