Is there any radiation when appliances are unplugged

Yes, but the harm is negligible.

For example, if a computer is unplugged and not turned on, the COMS module on the motherboard is still powered by a battery with a voltage of 3.3W, which only supplies power to this module to keep the computer's firmware settings (BIOS) from being lost. Both circuitry work, there will be radiation hazards, but this harm compared to the standby power supply circuit after plugging in, after the start of the various chip components work issued by the harmful radiation, the display of radiation compared to that can only be a drop in the bucket.