There’s a great discussion in Griffiths book on electromagnetism (typical book used for junior/senior course for physics majors) about what happens to free charges inside a conductor. He discusses how they will always find their way to the surface, distributing themselves to cancel the field inside the conductor. If they don’t do that, there will be a residual field to push more charges around. This happens until the field is totally cancelled. In a footnote he mentions how this surface effect only happens in 3D. In lower dimensions, like charges on a plate, say, the charges don’t necessarily go to the boundary.
Some neat simulations of both 3-D and 2-D cases.