a microcontoller pin stuck permanently at 0
Yes it is possible, even likely.

Most pins have overvoltage protection circuitry on them to keep small capacitive discharges from damaging the chip.  Sometimes the circuitry is more elaborate, but often there are simply reverse diodes to power and ground.

This means that when the power voltage is 0, the protection diode of a pin will conduct if the pin voltage would otherwise exceed the diode turnon voltage, around 600 mv.  Since that is a logic low level for just about any digital input, pins of unpowered micocontrollers on the same ground will read as low.

In general it is not good to allow too much current to flow thru the protection diodes.  If the diodes are beefy enough, then you can sometimes power up or partially power up the micro by forcing a I/O pin high.  However, expect it to act flaky.  Power current won't be flowing thru all the intended paths, and the power voltage will be one diode drop below whatever you are holding the pin at.  This also raises the whole power net the micro is connected to, which can have other unexpected consequences.  If the power net draws too much current, the diode will blow out.  Now the pin will be well above the power voltage of the micro, which probably damages a few more things in the micro.

Another issue is SCR latchup when real power is applied normally.  Due to how the chip is constructed and how the substrate is biased, current flowing into a pin while power is coming up can cause a sortof SCR latching effect.  This will draw lots more than the usual current of the micro, which can damage the micro, the power supply, or both.