Current Flow into MCU pin
Assuming you're talking about GPIO pins, it depends on how the pin is configured by the software. A pin configured as an input presents a high impedance, and very little current flows. A pin configured as an ​output and driven low presents a low impedance, and damaging current can flow.

This is why it's generally a good idea to use a series resistor to tie a pin high or low &mdash; if the pin is correctly configured, it has negligible effect, but if a software problem causes the pin to be misconfigured, it protects the MCU from damage.