Hello,
The chassis (equipment with PE, that is three terminal plug) is used for return current if a failure occurs (live wire connects to the chassis). The current flows back via the PE (protective earth) wire that is connected to the chassis. The fuse or residual current switch activates in case of faillure. If PE is not present in such case, there may be live voltage on the chassis (can be lethal).
The chassis is also the return current for the so-called Y interference supression capacitors. These capacitors are between the phases (or phase and neutral) and the chassis.
when you connect a device that requries protective earth to a socket without protective earth, and you touch it, current may flow through the Y capacitor(s) to the chassis and from the chassis through your own body to ground.
Consumer equipment has a limitation on the earth leakage current so that the shock will not be directly lethal, if there is an earth fault. However equipment for industrial use may have leakage current via the Y capacitors that can be above 3.5 mA. Such equipment may be used only with fixed wires and may require two earth paths to enhance safety.
Generally spoken, equipment that is equiped with PE should be used on a socket with PE only (I know that this isn't done always). The reason is that the strength of insulation in equipment with PE requirement is less then for equipment without PE requirement (such equipment requires double or reinforced insulation).