Why do electric lines of force not pass through conductor?

Ah but they DO! It is the action of electromagnetic lines of force (EMF) passing through a conductor that introduces current in the conductor. This is the basic principle behind electrical power generation.

Answer

The question relates to electric lines of force, not magnetic lines of force. Electric lines of force radiate perpendicularly from electric charge. As like electric charges distribute themselves evenly over the surface of a conductor, the electric lines of force radiate away from the surface of that conductor.