You need to check the datasheet for the specific MCU you are using.
Often/usually, the inputs are limited to the supply voltage rails. So if you run it at 2 Volts, the inputs must not exceed 2 volts.
But some MCU's have inputs, which can tolerate higher voltages, such as 5V or 3.3V. Again, best to refer to the datasheet.
If they do, be careful, because it may only apply to some of its inputs, and may have other requirements as well.
The problem is that many inputs have ESD/static protection built in to them, which means that there are diodes, connecting it (protecting it) to the ground and Vcc pins. They are connected up in such a way, that if more than about half a volt or so difference (below ground, or above Vcc), between the supply pins and the input(s), significant/huge currents can flow.
There is a good EEVblog video about it.