I am not sure how idiomatic it is. When someone says "stick your mouth to a hole" does he mean literally as in put your mouth in contact with the hole or close to it? I thought it was an exaggeration, but I am not sure if it is and if it is a commonly used phrase.
Here's an example of how I would use it:
The prisoner stuck his mouth to a hole on the door in order to be fed, because the guards wouldn't give them an utensil in fear that they would be used as a weapon or used to dig up a hole.