How or When does the facevalue of the share increase?

Are there any scenarios where there face value of the share increase?

Face value decreases on Forward Stock splits.

Face value increases on Reverse Stock Splits.

Bonus shares does not affect Face Value.

Had there ever been a instance of reverse stock splits
Yeah few small cap companies reverse split in order to meet exchange requirements.
Look at the link and check out companies old and new face values, example Vertex Spinning