Outputs are not the concern. What magic makes you think they are?

As for the regulator, some survive Vout > Vin; some don't. Understand the datasheet.

INPUT connections on IC devices should have proper termination, outputs not used should normally be open. Proper termination is either a zero or a one, for digital ICs. That varies with the technology and the device. For analog ICs look on the manufacturers data sheet, because it does matter.

 

Tony, using the 7805 or just 78 series regulator data sheet and regarding the diode bridging your regulator. Page 12 reads in part:
"9.2.2.2 Reverse-Bias Protection Occasionally, the input voltage to the regulator can collapse faster than the output voltage. This can occur, for example, when the input supply is crowbarred during an output overvoltage condition. If the output voltage is greater than approximately 7 V, the emitter-base junction of the series-pass element (internal or external) could break down and be damaged. To prevent this, a diode shunt can be used as shown in Figure 4". That being one application of a diode in a regulator circuit. There are more and another popular one is:
" 9.2.2.1 Operation With a Load Common to a Voltage of Opposite Polarity In many cases, a regulator powers a load that is not connected to ground but, instead, is connected to a voltage source of opposite polarity (e.g., operational amplifiers, level-shifting circuits, etc.). In these cases, a clamp diode should be connected to the regulator output as shown in Figure 3. This protects the regulator from output polarity reversals during startup and short-circuit operation".

Ron